Here are the essential concepts you must grasp in order to answer the question correctly.
Quadrantal Angles
Quadrantal angles are angles that lie on the axes of the Cartesian coordinate system, specifically 0°, 90°, 180°, and 270°. The sine and cosine values for these angles are well-defined and can be easily memorized: sin(0°) = 0, sin(90°) = 1, cos(0°) = 1, cos(90°) = 0, cos(180°) = -1, and sin(180°) = 0. Understanding these values is crucial for evaluating trigonometric expressions involving these angles.
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Trigonometric Function Values
Trigonometric functions, such as sine and cosine, relate the angles of a triangle to the ratios of its sides. For quadrantal angles, these functions yield specific values that simplify calculations. For example, sin(90°) = 1 and cos(180°) = -1. Knowing these values allows for straightforward evaluation of expressions involving trigonometric functions.
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Exponentiation in Trigonometric Expressions
Exponentiation in trigonometric expressions involves raising the function values to a power. For instance, (sin 90°)⁴ means taking the sine of 90°, which is 1, and raising it to the fourth power, resulting in 1. Similarly, (cos 180°)³ involves cubing the cosine value of 180°, which is -1, yielding -1. Understanding how to manipulate these powers is essential for correctly evaluating the overall expression.
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