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: 110


$\dfrac{\sqrt 3}{4}$

Work Step by Step

Recall the identity: $(f \cdot g) (x)=f(x) \cdot g(x)$ Let us consider that $f(x)=\sin x $ and $g(x)=\cos x$ We know from the unit circle that $\sin (\dfrac{4 \pi}{3}) =\dfrac{-\sqrt {3}}{2}$ and $\cos (\dfrac{4 \pi}{3})=\dfrac{-1}{2}$ Thus, we have: $(f \cdot g) (\dfrac{4 \pi}{3}) =\sin (\dfrac{4 \pi}{3}) \cdot \cos (\dfrac{4\pi}{3}) \\=\dfrac{-\sqrt {3}}{2} \cdot (\dfrac{-1}{2}) \\=\dfrac{\sqrt 3}{4}$
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