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 5 - Trigonometric Functions - Section 5.2 Trigonometric Functions: Unit Circle Approach - 5.2 Assess Your Understanding - Page 403: 102

Answer

$\dfrac{-1}{2}$

Work Step by Step

Let us consider $g( \theta)=\cos \theta$ When $\theta=60^{\circ}$, then $2 \theta=2 (60^{\circ})=120^{\circ}$ We know from the unit circle that $\cos (120^{\circ})=\cos (\dfrac{2\pi}{3})=\dfrac{-1}{2}$ The value of the cosine function is negative because the angle $(\dfrac{2\pi}{3})$ lies in the second quadrant. Thus, we have: $g(2\theta)=\cos (120^{\circ}) \\=\cos (\dfrac{2\pi}{3}) \\ =\dfrac{-1}{2}$
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