Chapter 7: Q. 87 (page 496)

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

Short Answer

Expert verified

The exact value is $\frac{1}{5}$

Step by step solution

Given information

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

Rewriting the inverse function

Rewriting, we get

$α = \cos^{- 1} \frac{3}{5} \cos α = \frac{3}{5}$

$\sin^{2} (\frac{1}{2} \cos^{- 1} \frac{3}{5}) = \sin^{2} \frac{α}{2} \sin^{2} (\frac{1}{2} \cos^{- 1} \frac{3}{5}) = {(\sin \frac{α}{2})}^{2}$

Using half angle formula and calculate

Using half angle, we get

$\sin \frac{α}{2} = \pm \sqrt{\frac{1 - \cos α}{2}} \sin \frac{α}{2} = \sqrt{\frac{1 - \cos α}{2}} \sin \frac{α}{2} = \sqrt{\frac{1 - \frac{3}{5}}{2}} \sin \frac{α}{2} = \sqrt{\frac{2}{10}} \sin \frac{α}{2} = \sqrt{\frac{1}{5}} \sin^{2} \frac{α}{2} = \frac{1}{5}$

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

Short Answer

Step by step solution

Given information

Rewriting the inverse function

Using half angle formula and calculate

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In Problems 79-90, find the exact value of each expression.sin212cos-135

Short Answer

Step by step solution

Given information

Rewriting the inverse function

Using half angle formula and calculate

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

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