Question

use an identity to write the expression as a single trigonometric function value or as a single number.
1/2 3/6 sin 74.7°
1/2 3/6 sin 74.7° = (simplify your answer. type an exact answer, using radicals as needed. do not include the degree symbol in your answer.)

Explanation:

Step1: Use the double - angle formula

Recall the double - angle formula \(\sin2\alpha = 2\sin\alpha\cos\alpha\), or \(\frac{1}{2}\sin2\alpha=\sin\alpha\cos\alpha\).
We are given \(\frac{1}{3}\sin74.7^{\circ}\frac{1}{2}\).
First, rewrite the expression as \(\frac{1}{6}\sin74.7^{\circ}\).
There is no trigonometric identity that can further simplify \(\sin74.7^{\circ}\) to a non - decimal, non - trigonometric form with the given operations.

Answer:

\(\frac{1}{6}\sin74.7^{\circ}\)