Chapter 7: Q. 79 (page 496)

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

Short Answer

Expert verified

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

Step by step solution

Given information

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

rewriting using implicit form

Rewriting, we get

$\sin (2 \sin^{- 1} \frac{1}{2}) = \sin (2 \frac{π}{6}) \sin (2 \sin^{- 1} \frac{1}{2}) = 2 \sin (\frac{π}{6}) \cos (\frac{π}{6}) \sin (2 \sin^{- 1} \frac{1}{2}) = 2 \times \frac{1}{2} \times \frac{\sqrt{3}}{2} \sin (2 \sin^{- 1} \frac{1}{2}) = \frac{\sqrt{3}}{2}$

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

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-112

Short Answer

Step by step solution

Given information

rewriting using implicit form

One App. One Place for Learning.

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