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

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

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

The given expression is:

$\csc [\cos^{- 1} (- \frac{\sqrt{3}}{2})]$

Let's take $θ = \cos^{- 1} (- \frac{\sqrt{3}}{2})$

$\cos θ = - \frac{\sqrt{3}}{2}$

$0 \leq θ \leq π$ is the domain of the function.

Step 2. Find the value of θ.

Initially, we have function $\cos^{- 1}$ and the bounds of cos function are going to be in the interval role="math" localid="1646466354693" $[0, π]$ . It represents the range of $\cos^{- 1}$ .

By using the unit circle, we can say that $θ$ must be equal to $\frac{5 π}{6}$ , so that we can get $- \frac{\sqrt{3}}{2}$ .

$\cos^{- 1} θ = - \frac{\sqrt{3}}{2} \cos^{- 1} (- \frac{\sqrt{3}}{2}) = \frac{5 π}{6}$

Step 3. Find the exact value of the expression.

$\csc [\cos^{- 1} (- \frac{\sqrt{3}}{2})] = \csc (\frac{5 π}{6}) \csc (θ) = \frac{1}{\sin θ} \csc (\frac{5 π}{6}) = \frac{1}{\sin (\frac{5 π}{6})}$

By using the unit circle, we know that $\sin (\frac{5 π}{6}) = \frac{1}{2}$

role="math" localid="1646466896004" $\csc (\frac{5 π}{6}) = \frac{1}{\frac{1}{2}} = 2$

Therefore, $\csc [\cos^{- 1} (- \frac{\sqrt{3}}{2})] = 2$ .

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

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

Step 1. Given information.

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In Problems 9–36, find the exact value of each expression.
$\csc [\cos^{- 1} (- \frac{\sqrt{3}}{2})]$