use an identity to write the expression as a single trigonometric function value or as a single number…

use an identity to write the expression as a single trigonometric function value or as a single number. \n1/2 3/6 sin 74.7° \n1/2 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.)

use an identity to write the expression as a single trigonometric function value or as a single number. \n1/2 3/6 sin 74.7° \n1/2 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.)

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})