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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 23 (page 485)

In problem 23-32,find the exact value of the each expression
$\sin 20 掳 \cos 10 掳 + \cos 20 掳 \sin 10 掳$

Short Answer

Expert verified

The exact value of $\sin 20 掳 \cos 10 掳 + \cos 20 掳 \sin 10 掳 = \frac{1}{2}$

Step by step solution

01

Step 1.Given information

The given expression $\sin 20 掳 \cos 10 掳 + \cos 20 掳 \sin 10 掳$

02

Step 2.Finding exact value of the given expression

The indicated expression $\sin 20 掳 \cos 10 掳 + \cos 20 掳 \sin 10 掳$ is in the form of the right side of the formula $\sin (伪 + 尾) = \sin 伪 \cos 尾 + \cos 伪 \sin 尾$

$\sin 20 掳 \cos 10 掳 + \cos 20 掳 \sin 10 掳 = \sin (20 掳 + 10 掳) = \sin (30 掳) = \frac{1}{2}$

Therefore,the exact value of $\sin 20 掳 \cos 10 掳 + \cos 20 掳 \sin 10 掳$ $= \frac{1}{2}$

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