Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 1 - Section 1.4 - Introduction to Identities - 1.4 Problem Set - Page 40: 34

Answer

$\cos\theta$ = - $\frac{2\sqrt 2}{3}$

Work Step by Step

We know from first Pythagorean identity that- $\cos\theta$ = ± $\sqrt (1-\sin^{2}\theta)$ As $\theta$ terminates in Q II, Therefore $\cos\theta$ will be negative- $\cos\theta$ = - $\sqrt (1-\sin^{2}\theta)$ substitute the given value of $\sin\theta$- $\cos\theta$ = - $\sqrt (1-(\frac{1}{3})^{2})$ $\cos\theta$ = - $\sqrt (1-\frac{1}{9})$ $\cos\theta$ = - $\sqrt (\frac{9 - 1}{9})$ = $\sqrt (\frac{8}{9})$ $\cos\theta$ = - $\frac{2\sqrt 2}{3}$
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