In Exercises 28–29, find a cofunction with the same value as the given expression. sin 70°

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, \(\theta = 70^\circ\).
3. Apply the cofunction identity by substituting \(\theta\) with \(70^\circ\): \(\sin 70^\circ = \cos(90^\circ - 70^\circ)\).
4. Simplify the expression inside the cosine: \(90^\circ - 70^\circ = 20^\circ\).
5. Write the final cofunction expression: \(\sin 70^\circ = \cos 20^\circ\).

Key Concepts

Cofunction Identity

Cofunction identities relate trigonometric functions of complementary angles, meaning angles that add up to 90°. For sine and cosine, sin(θ) = cos(90° - θ). This identity allows us to find a cofunction with the same value by subtracting the given angle from 90°.

Complementary Angles

Complementary angles are two angles whose measures add up to 90°. Understanding this concept is essential because cofunction identities depend on the relationship between complementary angles, enabling the conversion between sine and cosine values.

Evaluating Trigonometric Functions at Specific Angles

Evaluating trigonometric functions at specific angles, such as 70°, involves understanding angle measures and their corresponding function values. This skill helps in applying cofunction identities correctly to find equivalent expressions.