Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 7 - Trigonometric Identities and Equations - 7.6 Trigonometric Equations - 7.6 Exercises: 10

Answer

$\{0^{o}, \ \ 90^{o}, \ \ 180^{0} , \ \ 270^{o}\}$

Work Step by Step

As solved in exercise $4$, two angles (degree measures) with sine equal to 0 are $\{0^{o}, \ \ 180^{o}\}$ . Also, if $0 \leq \theta < 360^{o}\qquad/\times 2$ then $0 \leq 2\theta < 720^{o}.$ So either $2\theta= 0^{o}\quad$or$\quad 2\theta= 0^{o}+360^{o}$ or $2\theta= 180^{o}\quad$or$\quad 2\theta= 180^{o}+360$ $... $divide both sides by 2 in each equation $\theta= 0^{o}\quad$or$\quad \theta=180^{o}$ or $\theta=90^{o}\quad$or$\quad \theta= 90^{o}+180^{o}=270^{o}$ Solution set: $\{0^{o}, \ \ 90^{o}, \ \ 180^{0} , \ \ 270^{o}\}$.
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