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: 36


$\cos\theta$ = $\frac{3}{5}$

Work Step by Step

We know from first Pythagorean identity that- $\cos\theta$ = ± $\sqrt (1-\sin^{2}\theta)$ As $\theta$ terminates in Q IV, Therefore $\cos\theta$ will be positive- $\cos\theta$ = $\sqrt (1-\sin^{2}\theta)$ substitute the given value of $\sin\theta$- $\cos\theta$ = $\sqrt (1-(\frac{-4}{5})^{2})$ $\cos\theta$ = $\sqrt (1-\frac{16}{25})$ $\cos\theta$ = $\sqrt (\frac{25 - 16}{25})$ = $\sqrt (\frac{9}{25})$ $\cos\theta$ = $\frac{3}{5}$
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