Write each function value in terms of the cofunction of a complementary angle.
sin 98.0142°

Verified step by step guidance

1. Recall the cofunction identity for sine and cosine: \(\sin(\theta) = \cos(90^\circ - \theta)\), where angles are measured in degrees.
2. Identify the given angle \(\theta = 98.0142^\circ\) and recognize that the complementary angle to \(\theta\) is \(90^\circ - \theta\).
3. Calculate the complementary angle: \(90^\circ - 98.0142^\circ = -8.0142^\circ\).
4. Express \(\sin 98.0142^\circ\) in terms of the cosine of the complementary angle using the identity: \(\sin 98.0142^\circ = \cos(-8.0142^\circ)\).
5. Recall that cosine is an even function, so \(\cos(-x) = \cos x\), which means \(\sin 98.0142^\circ = \cos 8.0142^\circ\).

Key Concepts

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 allows expressing one function in terms of the cofunction of its complementary angle.

Complementary Angles

Two angles are complementary if their measures add up to 90°. Understanding this is essential because cofunction identities depend on this relationship to convert between sine, cosine, and other trigonometric functions.

Evaluating Trigonometric Functions at Specific Angles

Evaluating functions like sin 98.0142° involves recognizing that 98.0142° is greater than 90°, so rewriting it using complementary angles and cofunction identities simplifies the expression and aids in calculation or interpretation.