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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. 80 (page 496)

In Problems 79-90, find the exact value of each expression.
$\sin [2 \sin^{- 1} \frac{\sqrt{3}}{2}]$

Short Answer

Expert verified

The exact value is $\frac{\sqrt{3}}{2}$

Step by step solution

01

Given information

Given expression $\sin [2 \sin^{- 1} \frac{\sqrt{3}}{2}]$

02

Rewriting using implicit form

Rewriting, we get

$\sin [2 \sin^{- 1} \frac{\sqrt{3}}{2}] = \sin [2 \sin^{- 1} (\frac{蟺}{3})] \sin [2 \sin^{- 1} \frac{\sqrt{3}}{2}] = \sin [2 脳 60^{鈭�}] \sin [2 \sin^{- 1} \frac{\sqrt{3}}{2}] = \sin 120^{鈭�} \sin [2 \sin^{- 1} \frac{\sqrt{3}}{2}] = \frac{\sqrt{3}}{2}$

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