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

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Recall the cofunction identity for sine and cosine: \(\sin(\theta) = \cos(90^\circ - \theta)\), where angles are measured in degrees.

Identify the given angle \(\theta = 98.0142^\circ\) and recognize that the complementary angle to \(\theta\) is \(90^\circ - \theta\).

Calculate the complementary angle: \(90^\circ - 98.0142^\circ = -8.0142^\circ\).

Express \(\sin 98.0142^\circ\) in terms of the cosine of the complementary angle using the identity: \(\sin 98.0142^\circ = \cos(-8.0142^\circ)\).

Recall that cosine is an even function, so \(\cos(-x) = \cos x\), which means \(\sin 98.0142^\circ = \cos 8.0142^\circ\).

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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.

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Cofunction Identities

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.

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Intro to Complementary & Supplementary Angles

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.

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