{"type":"doc","content":[{"type":"paragraph","attrs":{"textAlign":null},"content":[{"type":"text","text":"{\"type\":\"doc\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q1. Convert the angle in radians to degrees: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{9\\\\pi}{5}\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\" radians\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Angle Conversion (Radians and Degrees)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to convert an angle from radians to degrees using the relationship between these two units.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Radians: A way to measure angles based on the radius of a circle.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Degrees: A common unit for measuring angles, where a full circle is 360 degrees.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Conversion formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Degrees} = \\\\text{Radians} \\\\times \\\\frac{180}{\\\\pi}\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Write the given angle: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{9\\\\pi}{5}\"}},{\"type\":\"text\",\"text\":\" radians.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Recall the conversion formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Degrees} = \\\\text{Radians} \\\\times \\\\frac{180}{\\\\pi}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Substitute \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{9\\\\pi}{5}\"}},{\"type\":\"text\",\"text\":\" for radians in the formula.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Simplify the expression by canceling \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\pi\"}},{\"type\":\"text\",\"text\":\" and multiplying the numbers.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: 324°\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{9\\\\pi}{5} \\\\times \\\\frac{180}{\\\\pi} = 324\"}},{\"type\":\"text\",\"text\":\" degrees.\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"The \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\pi\"}},{\"type\":\"text\",\"text\":\" cancels, and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"9 \\\\times 180 / 5 = 324\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q2. Convert the following angle in degrees to radians: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"25^{\\\\circ}\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Angle Conversion (Degrees to Radians)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to convert an angle from degrees to radians using the standard conversion formula.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Degrees: A unit for measuring angles.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Radians: The standard unit for measuring angles in mathematics.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Conversion formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Radians} = \\\\text{Degrees} \\\\times \\\\frac{\\\\pi}{180}\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Write the given angle: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"25^{\\\\circ}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Recall the conversion formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Radians} = \\\\text{Degrees} \\\\times \\\\frac{\\\\pi}{180}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Substitute $25"},{"type":"inlineMath","attrs":{"latex":" for degrees in the formula.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Simplify the expression to get the answer in terms of \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\pi\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{5\\\\pi}{36}\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\" radians\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"25 \\\\times \\\\frac{\\\\pi}{180} = \\\\frac{25\\\\pi}{180} = \\\\frac{5\\\\pi}{36}\"}},{\"type\":\"text\",\"text\":\" after simplifying the fraction.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q3. Find a positive angle less than \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"360^{\\\\circ}\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\" that is coterminal with \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-225^{\\\\circ}\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Coterminal Angles (Degrees)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your understanding of coterminal angles, which are angles that share the same terminal side when drawn in standard position.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Coterminal Angles: Angles that differ by a multiple of \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"360^{\\\\circ}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Coterminal Angle} = \\\\text{Given Angle} + 360^{\\\\circ} \\\\times n\"}},{\"type\":\"text\",\"text\":\", where \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"n\"}},{\"type\":\"text\",\"text\":\" is an integer.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Start with the given angle: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-225^{\\\\circ}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Add \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"360^{\\\\circ}\"}},{\"type\":\"text\",\"text\":\" repeatedly until the result is a positive angle less than $360^{\\\\circ}"}},{"type":"text","text":".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Check that your result is in the correct range (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"0^{\\\\circ} \\\\leq \\\\theta < 360^{\\\\circ}\"}},{\"type\":\"text\",\"text\":\").\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"135^{\\\\circ}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-225^{\\\\circ} + 360^{\\\\circ} = 135^{\\\\circ}\"}},{\"type\":\"text\",\"text\":\", which is positive and less than \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"360^{\\\\circ}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q4. Find a positive angle less than \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"2\\\\pi\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\" that is coterminal with \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{29\\\\pi}{8}\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Coterminal Angles (Radians)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to find coterminal angles in radians, specifically those between "},{"type":"inlineMath","attrs":{"latex":"0\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\" and $2\\\\pi\"}},{\"type\":\"text\",\"text\":\".\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Coterminal Angles: Angles that differ by a multiple of \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"2\\\\pi\"}},{\"type\":\"text\",\"text\":\" radians.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Formula: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\text{Coterminal Angle} = \\\\text{Given Angle} - 2\\\\pi \\\\times n\"}},{\"type\":\"text\",\"text\":\", where \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"n\"}},{\"type\":\"text\",\"text\":\" is an integer chosen so the result is in \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"[0, 2\\\\pi)\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Start with the given angle: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{29\\\\pi}{8}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Subtract \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"2\\\\pi\"}},{\"type\":\"text\",\"text\":\" as many times as needed to get an angle between $0\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\" and $2\\\\pi\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Express your answer as a simplified fraction in terms of \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\pi\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{13\\\\pi}{8}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{29\\\\pi}{8} - 2\\\\pi \\\\times 2 = \\\\frac{29\\\\pi}{8} - \\\\frac{32\\\\pi}{8} = -\\\\frac{3\\\\pi}{8}\"}},{\"type\":\"text\",\"text\":\", but since we want a positive angle, add \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"2\\\\pi\"}},{\"type\":\"text\",\"text\":\" (\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{16\\\\pi}{8}\"}},{\"type\":\"text\",\"text\":\") to get \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{13\\\\pi}{8}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q5. Suppose \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\triangle ABC\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\" is a right triangle with sides \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"a\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"b\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\", and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"c\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\" and right angle at \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"C\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\". Given \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"a = 7\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"c = 25\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\", find the unknown side "}},{"type":"text","text":"b"},{"type":"inlineMath","attrs":{"latex":" and the six trigonometric functions for angle \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"B\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\".\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Right Triangle Trigonometry\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to use the Pythagorean theorem to find a missing side and then express the six trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent) for a given angle in terms of side ratios.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Pythagorean Theorem: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"a^2 + b^2 = c^2\"}},{\"type\":\"text\",\"text\":\" (for right triangles)\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Trigonometric Ratios for angle \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"B\"}},{\"type\":\"text\",\"text\":\":\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sin B = \\\\frac{\\\\text{opposite}}{\\\\text{hypotenuse}}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cos B = \\\\frac{\\\\text{adjacent}}{\\\\text{hypotenuse}}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\tan B = \\\\frac{\\\\text{opposite}}{\\\\text{adjacent}}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\csc B = \\\\frac{1}{\\\\sin B}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sec B = \\\\frac{1}{\\\\cos B}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cot B = \\\\frac{1}{\\\\tan B}\"}}]}]}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Use the Pythagorean theorem to solve for \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"b\"}},{\"type\":\"text\",\"text\":\": \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"a^2 + b^2 = c^2\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Substitute \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"a = 7\"}},{\"type\":\"text\",\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"c = 25\"}},{\"type\":\"text\",\"text\":\" into the equation and solve for \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"b\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Once you have \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"b\"}},{\"type\":\"text\",\"text\":\", write the six trigonometric ratios for angle \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"B\"}},{\"type\":\"text\",\"text\":\" using the side lengths.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Express each ratio in simplest form, using radicals if necessary.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer:\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"b = 24\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sin B = \\\\frac{24}{25}\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cos B = \\\\frac{7}{25}\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\tan B = \\\\frac{24}{7}\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\csc B = \\\\frac{25}{24}\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sec B = \\\\frac{25}{7}\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cot B = \\\\frac{7}{24}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"These ratios are based on the side lengths found using the Pythagorean theorem.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q6. Given \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cos \\\\theta = -\\\\frac{3}{5}\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\theta\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\" is in Quadrant II, find the exact values of the remaining trigonometric functions.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Trigonometric Functions and Signs in Quadrants\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to use the Pythagorean identity and quadrant information to find all six trigonometric functions for a given angle.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Pythagorean Identity: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sin^2 \\\\theta + \\\\cos^2 \\\\theta = 1\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Signs of trig functions in Quadrant II: sine is positive, cosine and tangent are negative.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Definitions of tangent, cotangent, secant, and cosecant in terms of sine and cosine.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Start with \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cos \\\\theta = -\\\\frac{3}{5}\"}},{\"type\":\"text\",\"text\":\" and use the Pythagorean identity to solve for \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sin \\\\theta\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Since \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\theta\"}},{\"type\":\"text\",\"text\":\" is in Quadrant II, choose the positive value for \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sin \\\\theta\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Find \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\tan \\\\theta = \\\\frac{\\\\sin \\\\theta}{\\\\cos \\\\theta}\"}},{\"type\":\"text\",\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cot \\\\theta = \\\\frac{\\\\cos \\\\theta}{\\\\sin \\\\theta}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Find \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sec \\\\theta = \\\\frac{1}{\\\\cos \\\\theta}\"}},{\"type\":\"text\",\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\csc \\\\theta = \\\\frac{1}{\\\\sin \\\\theta}\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer:\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sin \\\\theta = \\\\frac{4}{5}\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\tan \\\\theta = -\\\\frac{4}{3}\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cot \\\\theta = -\\\\frac{3}{4}\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sec \\\\theta = -\\\\frac{5}{3}\"}},{\"type\":\"text\",\"text\":\", \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\csc \\\\theta = \\\\frac{5}{4}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Signs are determined by the quadrant, and values are found using the Pythagorean identity and definitions.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q7. Use reference angles to find the exact value of \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\tan 405^{\\\\circ}\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Reference Angles and Trigonometric Values\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to find the reference angle for an angle greater than \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"360^{\\\\circ}\"}},{\"type\":\"text\",\"text\":\" and use it to evaluate the tangent function.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Reference Angle: The acute angle formed by the terminal side of the given angle and the x-axis.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"To find the reference angle for \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\theta > 360^{\\\\circ}\"}},{\"type\":\"text\",\"text\":\", subtract \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"360^{\\\\circ}\"}},{\"type\":\"text\",\"text\":\" until the angle is between \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"0^{\\\\circ}\"}},{\"type\":\"text\",\"text\":\" and $360^{\\\\circ}"}},{"type":"text","text":".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Tangent values for common angles.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Subtract \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"360^{\\\\circ}\"}},{\"type\":\"text\",\"text\":\" from \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"405^{\\\\circ}\"}},{\"type\":\"text\",\"text\":\" to find the coterminal angle.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Determine the reference angle for the resulting angle.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Evaluate \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\tan\"}},{\"type\":\"text\",\"text\":\" at the reference angle, considering the quadrant for the sign.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\tan 405^{\\\\circ} = 1\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"The reference angle is \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"45^{\\\\circ}\"}},{\"type\":\"text\",\"text\":\", and tangent of "},{"type":"inlineMath","attrs":{"latex":"45^{\\\\circ}"}},{"type":"text","text":" is $1"},{"type":"inlineMath","attrs":{"latex":".\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q8. Use reference angles to find the exact value of \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cos \\\\left(\\\\frac{4\\\\pi}{3}\\\\right)\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Reference Angles and Trigonometric Values (Radians)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to find the reference angle in radians and use it to evaluate the cosine function.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Reference Angle: For angles in radians, subtract \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\pi\"}},{\"type\":\"text\",\"text\":\" or \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"2\\\\pi\"}},{\"type\":\"text\",\"text\":\" as needed to find the reference angle in \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"[0, \\\\frac{\\\\pi}{2}]\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Cosine values for common reference angles.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Find the reference angle for \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{4\\\\pi}{3}\"}},{\"type\":\"text\",\"text\":\" by subtracting \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\pi\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Determine the sign of cosine in the third quadrant.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Evaluate \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cos\"}},{\"type\":\"text\",\"text\":\" at the reference angle and apply the sign.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-\\\\frac{1}{2}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"The reference angle is \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{\\\\pi}{3}\"}},{\"type\":\"text\",\"text\":\", and cosine is negative in the third quadrant.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q9. Use reference angles to find the exact value of \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sin\\\\left(-\\\\frac{28\\\\pi}{3}\\\\right)\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Reference Angles and Trigonometric Values (Negative Angles)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to handle negative angles, find coterminal angles, and use reference angles to evaluate the sine function.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"To find a coterminal angle, add \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"2\\\\pi\"}},{\"type\":\"text\",\"text\":\" as many times as needed to get a positive angle.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Reference angle: The smallest positive angle between the terminal side and the x-axis.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Sine values for common reference angles.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Add \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"2\\\\pi\"}},{\"type\":\"text\",\"text\":\" repeatedly to \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-\\\\frac{28\\\\pi}{3}\"}},{\"type\":\"text\",\"text\":\" until you get an angle between $0\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\" and $2\\\\pi\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Find the reference angle for the resulting angle.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Evaluate \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sin\"}},{\"type\":\"text\",\"text\":\" at the reference angle, considering the sign based on the quadrant.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{\\\\sqrt{3}}{2}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"The reference angle is \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{\\\\pi}{3}\"}},{\"type\":\"text\",\"text\":\", and sine is positive in the appropriate quadrant.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q10. Use the unit circle to find the value of \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sin\\\\left(\\\\frac{5\\\\pi}{4}\\\\right)\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sin\\\\left(\\\\frac{21\\\\pi}{4}\\\\right)\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Unit Circle and Periodicity of Sine Function\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to use the unit circle to evaluate sine at various angles, including those greater than \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"2\\\\pi\"}},{\"type\":\"text\",\"text\":\".\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Unit Circle: A circle of radius 1 centered at the origin, used to define trigonometric functions.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Periodicity: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sin(\\\\theta + 2\\\\pi) = \\\\sin(\\\\theta)\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Reference angles and their sine values.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sin\\\\left(\\\\frac{5\\\\pi}{4}\\\\right)\"}},{\"type\":\"text\",\"text\":\", locate the angle on the unit circle and determine the sine value.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\sin\\\\left(\\\\frac{21\\\\pi}{4}\\\\right)\"}},{\"type\":\"text\",\"text\":\", subtract multiples of \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"2\\\\pi\"}},{\"type\":\"text\",\"text\":\" to find a coterminal angle between $0\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\" and $2\\\\pi\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Evaluate the sine at the coterminal angle.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-\\\\frac{\\\\sqrt{2}}{2}\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\" for both\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Both angles are coterminal with \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{5\\\\pi}{4}\"}},{\"type\":\"text\",\"text\":\", and the sine value is \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-\\\\frac{\\\\sqrt{2}}{2}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q11. Use the unit circle to find the value of \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cos\\\\left(\\\\frac{\\\\pi}{4}\\\\right)\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cos\\\\left(\\\\frac{17\\\\pi}{4}\\\\right)\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Unit Circle and Periodicity of Cosine Function\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to use the unit circle and periodicity to evaluate cosine at various angles.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Unit Circle: Used to find cosine values for standard angles.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Periodicity: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cos(\\\\theta + 2\\\\pi) = \\\\cos(\\\\theta)\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Reference angles and their cosine values.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cos\\\\left(\\\\frac{\\\\pi}{4}\\\\right)\"}},{\"type\":\"text\",\"text\":\", use the unit circle to find the value.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cos\\\\left(\\\\frac{17\\\\pi}{4}\\\\right)\"}},{\"type\":\"text\",\"text\":\", subtract \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"4\\\\pi\"}},{\"type\":\"text\",\"text\":\" to find a coterminal angle between $0\"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\" and $2\\\\pi\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Evaluate the cosine at the coterminal angle.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{\\\\sqrt{2}}{2}\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\" for both\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Both angles are coterminal with \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{\\\\pi}{4}\"}},{\"type\":\"text\",\"text\":\", and the cosine value is \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{\\\\sqrt{2}}{2}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q12. Use the unit circle to find the value of \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cos\\\\left(\\\\frac{7\\\\pi}{6}\\\\right)\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cos\\\\left(-\\\\frac{7\\\\pi}{6}\\\\right)\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Unit Circle and Even/Odd Properties of Cosine\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your understanding of the even property of cosine and how to evaluate cosine at negative angles.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Cosine is an even function: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cos(-\\\\theta) = \\\\cos(\\\\theta)\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Unit circle values for \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{7\\\\pi}{6}\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Find \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cos\\\\left(\\\\frac{7\\\\pi}{6}\\\\right)\"}},{\"type\":\"text\",\"text\":\" using the unit circle.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Use the even property to find \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\cos\\\\left(-\\\\frac{7\\\\pi}{6}\\\\right)\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Simplify the value as needed.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-\\\\frac{\\\\sqrt{3}}{2}\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\" for both\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Cosine is even, so the value is the same for both positive and negative angles.\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q13. Use the unit circle to find the value of \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\tan\\\\left(\\\\frac{3\\\\pi}{4}\\\\right)\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\tan\\\\left(\\\\frac{15\\\\pi}{4}\\\\right)\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Unit Circle and Periodicity of Tangent Function\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to use the unit circle and periodicity to evaluate tangent at various angles.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Periodicity: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\tan(\\\\theta + \\\\pi) = \\\\tan(\\\\theta)\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Unit circle values for \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{3\\\\pi}{4}\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Find \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\tan\\\\left(\\\\frac{3\\\\pi}{4}\\\\right)\"}},{\"type\":\"text\",\"text\":\" using the unit circle.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"For \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\tan\\\\left(\\\\frac{15\\\\pi}{4}\\\\right)\"}},{\"type\":\"text\",\"text\":\", subtract multiples of \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\pi\"}},{\"type\":\"text\",\"text\":\" to find a coterminal angle.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Evaluate the tangent at the coterminal angle.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-1\"}},{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\" for both\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Both angles are coterminal with \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{3\\\\pi}{4}\"}},{\"type\":\"text\",\"text\":\", and the tangent value is \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-1\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q14. Determine the amplitude and period of the function \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"y = 4 \\\\sin 2\\\\pi x\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Graphs of Sine Functions\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your understanding of how to find the amplitude and period of a sine function in the form \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"y = a \\\\sin(bx)\"}},{\"type\":\"text\",\"text\":\".\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Amplitude: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"|a|\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Period: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{2\\\\pi}{b}\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Identify the amplitude as the absolute value of the coefficient of sine.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Identify \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"b\"}},{\"type\":\"text\",\"text\":\" in \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"y = a \\\\sin(bx)\"}},{\"type\":\"text\",\"text\":\" and use the period formula.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Simplify the period expression as needed.\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer:\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Amplitude: $4"}},{"type":"text","text":"\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Period: $1"},{"type":"inlineMath","attrs":{"latex":"\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"The amplitude is the coefficient of sine, and the period is \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{2\\\\pi}{2\\\\pi} = 1\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q15. Determine the amplitude, period, and phase shift of \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"y = -3 \\\\cos(4x + \\\\pi)\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Graphs of Cosine Functions (Transformations)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your ability to identify amplitude, period, and phase shift for a transformed cosine function.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Amplitude: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"|a|\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Period: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{2\\\\pi}{b}\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Phase Shift: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-\\\\frac{c}{b}\"}},{\"type\":\"text\",\"text\":\" for \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"y = a \\\\cos(bx + c)\"}}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null},\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Identify the amplitude as the absolute value of the coefficient of cosine.\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Identify \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"b\"}},{\"type\":\"text\",\"text\":\" and \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"c\"}},{\"type\":\"text\",\"text\":\" in \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"y = a \\\\cos(bx + c)\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the period using \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{2\\\\pi}{b}\"}},{\"type\":\"text\",\"text\":\".\"}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Calculate the phase shift using \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-\\\\frac{c}{b}\"}},{\"type\":\"text\",\"text\":\".\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Try solving on your own before revealing the answer!\"}]},{\"type\":\"collapsible\",\"content\":[{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Final Answer:\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Amplitude: $3"}},{"type":"text","text":"\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Period: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{\\\\pi}{2}\"}}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Phase Shift: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"-\\\\frac{\\\\pi}{4}\"}}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":3},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Q16. Graph two periods of the tangent function \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"y = \\\\tan\\\\left(x - \\\\frac{\\\\pi}{14}\\\\right)\"}}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Background\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Topic: Graphs of Tangent Functions (Transformations)\"}]},{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"This question tests your understanding of the period and phase shift of the tangent function and how to graph it over two periods.\"}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"underline\"}],\"text\":\"Key Terms and Formulas\"}]},{\"type\":\"bulletList\",\"content\":[{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Period of tangent: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\pi\"}}]}]},{\"type\":\"listItem\",\"content\":[{\"type\":\"paragraph\",\"attrs\":{\"textAlign\":null},\"content\":[{\"type\":\"text\",\"text\":\"Phase shift: \"},{\"type\":\"inlineMath\",\"attrs\":{\"latex\":\"\\\\frac{\\\\pi}{14}\"}},{\"type\":\"text\",\"text\":\" to the right\"}]}]}]},{\"type\":\"heading\",\"attrs\":{\"textAlign\":null,\"level\":4},\"content\":[{\"type\":\"text\",\"marks\":[{\"type\":\"bold\"}],\"text\":\"Step-by-Step Guidance\"}]},{\"type\":\"orderedList\",\"attrs\":{\"start\":1,\"type\":null}