Find a cofunction with the same value as the given expression.
sin 19°

Key Concepts

Cofunction Identities

Cofunction identities in trigonometry relate the values of trigonometric functions of complementary angles. Specifically, for any angle θ, the sine of θ is equal to the cosine of its complement: sin(θ) = cos(90° - θ). This means that for sin(19°), the cofunction is cos(90° - 19°), which simplifies to cos(71°).

Complementary Angles

Complementary angles are two angles whose measures add up to 90 degrees. In the context of trigonometric functions, this relationship is crucial for understanding cofunction identities. For example, if one angle is 19°, its complement is 71°, and the sine of 19° can be expressed in terms of the cosine of 71°.

Trigonometric Functions

Trigonometric functions, such as sine, cosine, and tangent, are fundamental in relating angles to side lengths in right triangles. The sine function specifically measures the ratio of the length of the opposite side to the hypotenuse. Understanding these functions is essential for solving problems involving angles and their relationships, such as finding cofunctions.