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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. 81 (page 496)

In Problems 79-90, find the exact value of each expression.
$\cos (2 \sin^{- 1} \frac{3}{5})$

Short Answer

Expert verified

The exact value is $\frac{7}{25}$

Step by step solution

01

Given information

Given expression $\cos (2 \sin^{- 1} \frac{3}{5})$

02

Assume θ=sin-135 and use double angle formula

Using double angle, we get

$\cos (2 胃) = 1 - 2 {(\frac{3}{5})}^{2} \cos (2 胃) = 1 - 2 路 \frac{9}{25} \cos (2 胃) = \frac{7}{25}$

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