Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

In Problems 9–36, find the exact value of each expression.
$\tan [\sin^{- 1} (- \frac{1}{2})]$

The value of the expression $\tan [\sin^{- 1} (- \frac{1}{2})] = - \frac{\sqrt{3}}{3}$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

The given expression is:

$\tan [\sin^{- 1} (- \frac{1}{2})]$

Let's take localid="1646413783497" $θ = \sin^{- 1} (- \frac{1}{2})$

$\sin θ = - \frac{1}{2}$

$- \frac{π}{2} \leq θ \leq \frac{π}{2}$ is the domain of the function.

Step 2. Find the value of θ.

Initially, we have $\sin^{- 1}$ and the bounds of sin function are going to be in the interval $[- \frac{π}{2}, \frac{π}{2}]$ . It represents the range of $\sin^{- 1}$ .

By using the unit circle, we can say that $θ$ must be equal to $- \frac{π}{6}$ , so that we can get $- \frac{1}{2}$ .

$\sin θ = - \frac{1}{2} \sin^{- 1} (- \frac{1}{2}) = - \frac{π}{6}$

Step 3. Find the exact value of the expression.

$\tan (- \frac{π}{6}) = - \frac{\sqrt{3}}{3}$

Therefore, role="math" localid="1646414553456" $\tan [\sin^{- 1} (- \frac{1}{2})] = - \frac{\sqrt{3}}{3}$ .

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 9–36, find the exact value of each expression.
$\tan [\sin^{- 1} (- \frac{1}{2})]$

Step by Step Solution

Step 1. Given information.

Step 2. Find the value of θ.

Step 3. Find the exact value of the expression.

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Step by Step Solution

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In Problems 9–36, find the exact value of each expression.
$\tan [\sin^{- 1} (- \frac{1}{2})]$