Q 19. In Problems 9鈥�36, find the exa... [FREE SOLUTION]

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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 19. (page 457)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

The given expression is:

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

Let's take $胃 = \sin^{- 1} (- \frac{1}{2})$

$\sin 胃 = (- \frac{1}{2})$

$- \frac{蟺}{2} 鈮� 胃鈮� \frac{蟺}{2}$ is the domain of the function.

Step 2. Find the value of θ.

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

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

$\sin 胃 = - \frac{1}{2} \sin^{- 1} (- \frac{1}{2}) = - \frac{蟺}{6}$

Step 3. Find the exact value of the expression.

$\sec [\sin^{- 1} (- \frac{1}{2})] = \sec (- \frac{蟺}{6}) \sec (胃) = \frac{1}{\cos 胃} \sec (- \frac{蟺}{6}) = \frac{1}{\cos (- \frac{蟺}{6})}$

By using the unit circle, we know that $\cos (- \frac{蟺}{6}) = \frac{\sqrt{3}}{2}$ , then

localid="1646454996847" $\sec (- \frac{蟺}{6}) = \frac{1}{\frac{\sqrt{3}}{2}} \sec (- \frac{蟺}{6}) = \frac{2}{\sqrt{3}} \sec (- \frac{蟺}{6}) = \frac{2}{\sqrt{3}} 路 \frac{\sqrt{3}}{\sqrt{3}} \sec (- \frac{蟺}{6}) = \frac{2 \sqrt{3}}{3}$

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

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91影视

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the value of θ.

Step 3. Find the exact value of the expression.

One App. One Place for Learning.

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In Problems 9鈥�36, find the exact value of each expression.secsin-1-12

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the value of θ.

Step 3. Find the exact value of the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Theoretical and Mathematical Physics

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