Question

write the function value in terms of the cofunction of a complementary angle.
sin 173°27
sin 173°27 = □(□°□)
(simplify your answers. type the cofunction abbreviation in the first input box. type the degree part of the angle measure in the second input box. type the minute part of the angle measure in the third input box.)

Explanation:

Step1: Recall the co - function identity

The co - function identity for sine and cosine is \(\sin\theta=\cos(90^{\circ}-\theta)\). But here \(\theta = 173^{\circ}27'\), and we know that \(\sin\alpha=\cos(90^{\circ}-\alpha + 180^{\circ}n)\) (using the periodicity and co - function properties of trigonometric functions). In fact, \(\sin\theta=\cos(270^{\circ}-\theta)\) (since \(\sin\theta=\cos(90^{\circ}-\theta + 180^{\circ})\)).
Substitute \(\theta = 173^{\circ}27'\) into the formula \(\sin\theta=\cos(270^{\circ}-\theta)\).

Step2: Calculate \(270^{\circ}-\theta\)

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Answer:

\(\cos(96^{\circ}33')\)