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

Given information

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

Rewriting using implicit form

Rewriting, we get

$\sin [2 \sin^{- 1} \frac{\sqrt{3}}{2}] = \sin [2 \sin^{- 1} (\frac{π}{3})] \sin [2 \sin^{- 1} \frac{\sqrt{3}}{2}] = \sin [2 \times 60^{\circ}] \sin [2 \sin^{- 1} \frac{\sqrt{3}}{2}] = \sin 120^{\circ} \sin [2 \sin^{- 1} \frac{\sqrt{3}}{2}] = \frac{\sqrt{3}}{2}$

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

Short Answer

Step by step solution

Given information

Rewriting using implicit form

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In Problems 79-90, find the exact value of each expression.sin2sin-132

Short Answer

Step by step solution

Given information

Rewriting using implicit form

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