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 for sine and cosine: \(\sin(\theta) = \cos(90^\circ - \theta)\), where the angles are complementary (sum to \(90^\circ\)).
2. Identify the complementary angle for \(15^\circ\) by subtracting it from \(90^\circ\): \(90^\circ - 15^\circ = 75^\circ\).
3. Rewrite \(\sin 15^\circ\) using the cofunction identity as \(\cos(75^\circ)\).
4. Thus, \(\sin 15^\circ\) is expressed in terms of the cosine of its complementary angle: \(\cos(75^\circ)\).
5. This approach can be applied to other trigonometric functions using their respective cofunction identities.

Key Concepts

Cofunction Identity

Cofunction identities relate trigonometric functions of complementary angles, where the sum of the angles is 90°. For example, sin(θ) = cos(90° - θ). This means the sine of an angle equals the cosine of its complement, which is essential for rewriting sin 15° in terms of a cosine function.

Complementary Angles

Complementary angles are two angles whose measures add up to 90°. Understanding this concept is crucial because cofunction identities depend on the relationship between an angle and its complement, allowing conversion between sine and cosine functions.

Basic Trigonometric Functions

Sine and cosine are fundamental trigonometric functions that relate angles to ratios of sides in a right triangle. Knowing their definitions and properties helps in applying cofunction identities and expressing one function in terms of another.