What is the complementary angle identity for sine?

The complementary angle identity for sine states that the sine of an angle is equal to the cosine of its complementary angle. Specifically, this identity can be written as sin[(π/2) - x] = cos(x).

This relationship stems from the fact that two angles are complementary if the sum of their measures is 90 degrees (or π/2 radians in radian measure). As a result, when you take the sine of an angle that is subtracted from π/2, it gives you the cosine of the original angle. This identity is fundamental in trigonometry and helps in simplifying expressions and solving equations involving sine and cosine.

Understanding this identity is crucial as it allows for the transformation of functions and provides insights into the relationships between different trigonometric functions. The other options do not represent the complementary angle identity for sine, thereby affirming the correctness of the answer provided.