In Exercises 31–38, find a cofunction with the same value as the given expression. sin 7°

Verified step by step guidance

1. Recall the cofunction identity for sine and cosine: \(\sin(\theta) = \cos(90^\circ - \theta)\).
2. Identify the angle in the given expression: here, \(\theta = 7^\circ\).
3. Apply the cofunction identity by substituting \(\theta\) with \(7^\circ\) to find the equivalent cosine expression.
4. Write the cofunction expression as \(\cos(90^\circ - 7^\circ)\).
5. Simplify the angle inside the cosine function to get \(\cos(83^\circ)\), which is the cofunction with the same value as \(\sin 7^\circ\).

Key Concepts

Cofunction Identity

Cofunction identities relate the trigonometric functions of complementary angles, meaning angles that add up to 90°. For sine and cosine, the identity is sin(θ) = cos(90° - θ). This allows us to express sine values in terms of cosine and vice versa.

Complementary Angles

Complementary angles are two angles whose measures add up to 90°. Understanding this concept is essential because cofunction identities rely on the relationship between an angle and its complement to find equivalent trigonometric values.

Trigonometric Function Values

Knowing how to evaluate or manipulate trigonometric functions like sine and cosine is crucial. Recognizing that sin 7° can be rewritten using a cofunction identity helps simplify expressions or solve equations involving trigonometric values.