Trigonometry (10th Edition)

Published by Pearson

Chapter 2 - Acute Angles and Right Triangles - Section 2.1 Trigonometric Functions of Acute Angles - 2.1 Exercises: 33

Answer

$\theta$ = 20$^{\circ}$

Work Step by Step

$\sin$ (2$\theta$ + 10$^{\circ}$) = $\cos$ (3$\theta$ - 20$^{\circ}$) According to Cofunction Identities $\sin$ (2$\theta$ + 10$^{\circ}$) = $\cos$ (3$\theta$ - 20$^{\circ}$) is true only if the sum of the angles is 90$^{\circ}$. Therefore: (2$\theta$ + 10$^{\circ}$) + (3$\theta$ - 20$^{\circ}$) = 90$^{\circ}$ 5$\theta$ - 10$^{\circ}$ = 90$^{\circ}$ 5$\theta$ = 100$^{\circ}$ $\theta$ = 20$^{\circ}$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.