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

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Recall the cofunction identity for sine and cosine: \(\sin(\theta) = \cos(90^\circ - \theta)\), where the angles are complementary (sum to \(90^\circ\)).

Identify the complementary angle for \(15^\circ\) by subtracting it from \(90^\circ\): \(90^\circ - 15^\circ = 75^\circ\).

Rewrite \(\sin 15^\circ\) using the cofunction identity as \(\cos(75^\circ)\).

Thus, \(\sin 15^\circ\) is expressed in terms of the cosine of its complementary angle: \(\cos(75^\circ)\).

This approach can be applied to other trigonometric functions using their respective cofunction identities.

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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.

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Cofunction Identities

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.

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Intro to Complementary & Supplementary Angles

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.

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