Given a right triangle where angle has an opposite side of length , an adjacent side of length , and a hypotenuse of length , use the triangle to evaluate each function: , , and .
Table of contents
- 0. Review of College Algebra4h 45m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
2. Trigonometric Functions on Right Triangles
Trigonometric Functions on Right Triangles
Multiple Choice
Omar wants to determine in a right triangle. If the length of the adjacent side to angle is 5 units and the hypotenuse is 13 units, what is ?
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Verified step by step guidance1
Recall the definition of cosine in a right triangle: \(\cos \theta = \frac{\text{length of adjacent side}}{\text{length of hypotenuse}}\).
Identify the given values from the problem: the adjacent side to angle \(\theta\) is 5 units, and the hypotenuse is 13 units.
Substitute the given values into the cosine formula: \(\cos \theta = \frac{5}{13}\).
Simplify the fraction if possible (in this case, \(\frac{5}{13}\) is already in simplest form).
Conclude that \(\cos \theta\) is the ratio of the adjacent side over the hypotenuse, which is \(\frac{5}{13}\).
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