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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. 83 (page 496)

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

Short Answer

Expert verified

The exact value is $\frac{24}{7}$

Step by step solution

01

Given information

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

02

Rewrite the inverse function and calculate the opposite side

Rewriting, we get

$胃 = \cos^{- 1} (- \frac{3}{5}) c = \sqrt{5^{2} - 3^{2}} c = \sqrt{25 - 9} c = \sqrt{16} c = 4$

03

Calculate tangent and use double angle formula

Calculating, we get

$\tan 胃 = - \frac{4}{3} \tan (2 胃) = \frac{2 (- \frac{4}{3})}{1 - {(- \frac{4}{3})}^{2}} \tan (2 胃) = \frac{- \frac{8}{3}}{1 - \frac{16}{9}} \tan (2 胃) = \frac{- \frac{8}{3}}{- \frac{7}{9}} \tan (2 胃) = \frac{24}{7}$

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Most popular questions from this chapter

The distance $d$ from the point $(2, - 3)$ to the point $(5, 1)$ is ______.

Show that $\tan^{- 1} (\frac{1}{v}) = \frac{蟺}{2} - \tan^{- 1} v$ , if $v > 0$

Establish each identity.

$\frac{1 + \sin 胃 + \cos 胃}{1 + \sin 胃 - \cos 胃} = \frac{1 + \cos 胃}{\sin 胃}$

Establish each identity.

$\frac{1 + \sin 胃}{1 - \sin 胃} - \frac{1 - \sin 胃}{1 + \sin 胃} = 4 \tan 胃 s e c 胃$

Multiply: $\frac{\cos (胃)}{1 - \sin (胃)} \frac{1 + \sin (胃)}{1 + \sin (胃)}$

See all solutions

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