Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 7 - Applications of Trigonometric Functions - Section 7.1 Right Triangle Trigonometry ; Applications - 7.1 Assess Your Understanding - Page 540: 23



Work Step by Step

Recall the co-function identity: $ \sin (\theta)=\cos(90^{\circ}-\theta)$ We know that $\sin^2 \theta+\cos^2 \theta=1$ Therefore, $1-\cos^2 \ (20^{\circ})-\cos^2 (70^{\circ}) =1-\cos^2 \ (20^{\circ})-\sin^2 (70^{\circ}) \\=1-[\cos^2 \ (20^{\circ})+\sin^2 (20^{\circ})] \\=1-1 \\=0$
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