Write each function value in terms of the cofunction of a complementary angle.
sin 15°

Verified step by step guidance

1. Recall the cofunction identity: \( \sin(\theta) = \cos(90^\circ - \theta) \).
2. Identify the given angle \( \theta = 15^\circ \).
3. Substitute \( \theta = 15^\circ \) into the cofunction identity: \( \sin(15^\circ) = \cos(90^\circ - 15^\circ) \).
4. Simplify the expression inside the cosine function: \( 90^\circ - 15^\circ = 75^\circ \).
5. Express \( \sin(15^\circ) \) in terms of the cofunction: \( \sin(15^\circ) = \cos(75^\circ) \).

Key Concepts

Cofunction Identities

Cofunction identities relate the trigonometric functions of complementary angles. For example, the sine of an angle is equal to the cosine of its complement: sin(θ) = cos(90° - θ). This relationship is crucial for expressing trigonometric functions in terms of their cofunctions, particularly when dealing with angles that sum to 90 degrees.

Complementary Angles

Complementary angles are two angles whose measures add up to 90 degrees. In trigonometry, understanding complementary angles is essential for applying cofunction identities. For instance, if you have an angle of 15°, its complement is 75°, which can be used to express trigonometric functions in a different form.

Trigonometric Functions

Trigonometric functions, such as sine, cosine, and tangent, are fundamental in trigonometry, representing the ratios of sides in a right triangle. Each function has specific properties and relationships, including the ability to express one function in terms of another using identities. This is particularly useful when simplifying expressions or solving equations involving angles.