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 6 - Analytic Trigonometry - Section 6.5 Sum and Difference Formulas - 6.5 Assess Your Understanding - Page 508: 23

Answer

$$\dfrac{1}{2}$$

Work Step by Step

We apply the sum formula: $\sin(A+B)=\sin(A)\cos(B)+\cos(A)\sin(B)$ Therefore, $$\sin(20^\circ) \ \cos(10^\circ)+\cos(10^\circ) \ \sin(20^\circ)\\ =\sin \ (20^\circ+10^\circ)\\ =\sin \ (30^\circ)\\ =\dfrac{1}{2}$$
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