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: \( \sin(\theta) = \cos(90^\circ - \theta) \).
2. Identify the given angle \( \theta = 70^\circ \).
3. Substitute \( \theta = 70^\circ \) into the cofunction identity: \( \sin(70^\circ) = \cos(90^\circ - 70^\circ) \).
4. Simplify the expression inside the cosine function: \( 90^\circ - 70^\circ = 20^\circ \).
5. Conclude that the cofunction with the same value is \( \cos(20^\circ) \).

Key Concepts

Cofunction Identities

Cofunction identities in trigonometry relate the sine and cosine functions of complementary angles. Specifically, the sine of an angle is equal to the cosine of its complement, expressed as sin(θ) = cos(90° - θ). This relationship is fundamental for finding cofunctions that yield the same value for given angles.

Complementary Angles

Complementary angles are two angles whose measures add up to 90 degrees. In the context of trigonometric functions, if one angle is known, its complement can be easily calculated. Understanding complementary angles is essential for applying cofunction identities effectively.

Trigonometric Functions

Trigonometric functions, such as sine, cosine, and tangent, are fundamental in relating angles to side lengths in right triangles. Each function has specific properties and values based on the angle's measure. Familiarity with these functions is crucial for solving problems involving angle relationships and cofunctions.