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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. 62 (page 504)

In Problems $58 - 63$ , find the exact value of each expression.
$\sin [2 \cos^{- 1} (\frac{- 3}{5})]$ .

Short Answer

Expert verified

The exact value of the expression $\sin [2 \cos^{- 1} (\frac{- 3}{5})]$ is, $\frac{- 24}{25}$ .

Step by step solution

01

Step 1 Given equation is,

$\sin [2 \cos^{- 1} (\frac{- 3}{5})]$ .

Let $胃 = \cos^{- 1} (\frac{- 3}{5})$

$\cos 胃 = \frac{- 3}{5}$

we know that, $\sin 胃 = \sqrt{1 - \cos^{2} 胃}$

substitute the known values in the formula.

$\sin 胃 = \sqrt{1 - {(\frac{- 3}{5})}^{2}} = \sqrt{1 - \frac{9}{25}} \sin 胃 = \frac{4}{5}$

02

Step 2 we know that sin 2θ=2 sin θ cos θ

Substitute the known values in the formula.

$\sin (2 胃) = 2 . \frac{4}{5} . \frac{- 3}{5} = - \frac{24}{25} \sin [2 \cos^{- 1} (\frac{- 3}{5})] = - \frac{24}{25}$

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Most popular questions from this chapter

express each product as a sum containing only sines or only cosines

$\sin \frac{蠎}{2} \cos \frac{5 蠎}{2}$

Establish each identity.

$s e c 胃 - \cos 胃 = \sin 胃 \tan 胃$

Establish each identity.

$\frac{1 + \cos 胃 + \sin 胃}{1 + \cos 胃 - \sin 胃} = s e c 胃 + \tan 胃$

If $z = \tan \frac{伪}{2}$ , show that localid="1646416257885" $\cos 伪 = \frac{1 - z^{2}}{1 + z^{2}}$ .

Find the value of the number C:

$\frac{1}{2} \cos^{2} x + C = \frac{1}{4} \cos (2 x)$

See all solutions

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