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

Verified step by step guidance

1. Identify the cofunction identity for sine: \( \sin(\theta) = \cos(90^\circ - \theta) \).
2. Recognize that the angle given is \( 98.0142^\circ \).
3. Determine the complementary angle by subtracting the given angle from \( 90^\circ \): \( 90^\circ - 98.0142^\circ \).
4. Calculate the complementary angle: \( 90^\circ - 98.0142^\circ = -8.0142^\circ \).
5. Express \( \sin 98.0142^\circ \) in terms of its cofunction: \( \cos(-8.0142^\circ) \).

Key Concepts

Cofunction Identities

Cofunction identities in trigonometry relate the values of trigonometric functions of complementary angles. For example, the sine of an angle is equal to the cosine of its complement: sin(θ) = cos(90° - θ). This relationship is crucial for rewriting trigonometric functions in terms of their cofunctions, especially when dealing with angles that sum to 90 degrees.

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, the other can be easily determined. Understanding complementary angles is essential for applying cofunction identities effectively, as it allows for the transformation of functions based on their angle relationships.

Angle Measurement

Angle measurement can be expressed in degrees or radians, with degrees being the more common unit in basic trigonometry. In this question, the angle 98.0142° exceeds 90 degrees, indicating that it is not directly complementary to another angle. Recognizing how to convert or relate angles greater than 90 degrees to their complementary counterparts is important for applying trigonometric identities correctly.