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: 101


$\dfrac{\sqrt 3}{2}$

Work Step by Step

Let us consider: $f(\theta)=\sin \theta$ When $\theta=60^{\circ}$, then $2 \theta=2 (60^{\circ})=124^{\circ}$ We know from the unit circle that $\sin (120^{\circ})=\sin (\dfrac{2\pi}{3})=\dfrac{\sqrt 3}{2}$ Thus, we have: $f(2\theta)=\sin (120^{\circ}) \\=\sin\dfrac{2\pi}{3} \\ =\dfrac{\sqrt 3}{2}$
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