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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. 88 (page 496)

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

Short Answer

Expert verified

The exact value is $\frac{9}{10}$

Step by step solution

01

Given information

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

02

Use half angle formula and calculate

Here,

$\cos^{2} (\frac{胃}{2}) = \frac{1 + \cos 胃}{2} \cos (\cos^{- 1} x) = x \cos^{- 1} x = \sin^{- 1} (\sqrt{1 - x^{2}}) a = \cos^{2} (\frac{1}{2} \sin^{- 1} (\frac{3}{5})) 胃 = \sin^{- 1} (\frac{3}{5}) 胃 = \cos^{- 1} (\frac{4}{5})$

03

Calculating using half angle formula

Calculating, we get

$a = \cos^{2} (\frac{1}{2} \sin^{- 1} (\frac{3}{5})) a = \frac{1 + \cos (\cos^{- 1} (\frac{4}{5}))}{2} a = = \frac{1 + \frac{4}{5}}{2} a = \frac{9}{10}$

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