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: 6

Answer

$\{135^{o}, \ \ 225^{o}\}$

Work Step by Step

For a point on the unit circle, the coordinates are ($\cos\theta,\sin\theta),\ \quad \theta\in[0^{o},360^{o})$ To solve the problem, find the points for which the $x$-coordinate is $-\displaystyle \frac{\sqrt{2}}{2},\ \quad$($\displaystyle \cos\theta=-\frac{\sqrt{2}}{2}$). Using the given unit circle, we find two such points, in quadrant II, for $\theta=135^{o}$ in quadrant III, for $\theta=225^{o}$ Solution set: $\{135^{o}, \ \ 225^{o}\}$
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