Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2. tan 25.4°

Verified step by step guidance

1. Recall the cofunction identity for tangent: \( \tan(\theta) = \cot(90^\circ - \theta) \). This means the tangent of an angle is equal to the cotangent of its complement.
2. Identify the given angle \( \theta = 25.4^\circ \). Since the angles are acute, the complement is \( 90^\circ - 25.4^\circ \).
3. Calculate the complement angle: \( 90^\circ - 25.4^\circ = 64.6^\circ \).
4. Rewrite \( \tan 25.4^\circ \) using the cofunction identity as \( \cot 64.6^\circ \).
5. Thus, \( \tan 25.4^\circ \) expressed in terms of its cofunction is \( \cot 64.6^\circ \).

Key Concepts

Trigonometric Functions

Trigonometric functions like sine, cosine, and tangent relate the angles of a right triangle to the ratios of its sides. Tangent of an angle is the ratio of the opposite side to the adjacent side. Understanding these functions is essential for manipulating and converting between them.

Cofunction Identities

Cofunction identities express a trigonometric function of an angle in terms of the complementary angle's cofunction. For acute angles, tan(θ) = cot(90° - θ), meaning the tangent of an angle equals the cotangent of its complement. This relationship helps rewrite functions in terms of their cofunctions.

Complementary Angles

Complementary angles are two angles whose measures add up to 90°. In trigonometry, many identities rely on this concept, especially cofunction identities. Recognizing that 25.4° and 64.6° are complementary allows rewriting tan 25.4° as cot 64.6°.