Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.3 Trigonometric Equations II - 6.3 Exercises - Page 273: 10

Answer

The solution set is $$\{0^\circ, 60^\circ,120^\circ, 180^\circ, 240^\circ, 300^\circ\}$$

Work Step by Step

$$\sin3\theta=0$$ over interval $[0^\circ,360^\circ)$ 1) Find corresponding interval for $3\theta$ The interval for $\theta$ is $[0^\circ,360^\circ)$, which can also be written as the inequality: $$0^\circ\le\theta\lt360^\circ$$ Therefore, for $3\theta$, the inequality would be $$0^\circ\le3\theta\lt1080^\circ$$ Thus, the corresponding interval for $3\theta$ is $[0^\circ,1080^\circ)$. 2) Now we examine the equation: $$\sin3\theta=0$$ Over interval $[0^\circ,1080^\circ)$, there are 6 values whose sine equals $0$, which are $\{0^\circ, 180^\circ, 360^\circ,540^\circ, 720^\circ, 900^\circ\}$ Therefore, $$3\theta=\{0^\circ, 180^\circ, 360^\circ,540^\circ, 720^\circ, 900^\circ\}$$ It follows that $$\theta=\{0^\circ, 60^\circ,120^\circ, 180^\circ, 240^\circ, 300^\circ\}$$ This is the solution set of the equation.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

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.