Trigonometry 7th Edition

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

Chapter 1 - Test - Page 51: 27

Answer

2 $|\cos\theta|$

Work Step by Step

Given expression- $ \sqrt {4 - x^{2}}$ Substituting $2\sin\theta$ for $x$ as given, the expression becomes- $ \sqrt {4 - (2\sin\theta)^{2}}$ = $ \sqrt {4 -4\sin^{2}\theta}$ = $ \sqrt {4(1 - \sin^{2}\theta)}$ = $ \sqrt {4\cos^{2}\theta}$ { Writing $(1 - \sin^{2}\theta)$ as $ \cos^{2}\theta$ using first Pythagorean identity} = 2 $|\cos\theta|$
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