Chapter 7: Q 13. (page 457)

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

Short Answer

Expert verified

The value of the expression $\sec (\cos^{- 1} \frac{1}{2}) = 2$

Step by step solution

Step 1. Given information.

The given expression is:

$\sec (\cos^{- 1} \frac{1}{2})$

Let's take $θ = \cos^{- 1} \frac{1}{2}$ ,

$\cos θ = \frac{1}{2}$

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

Step 2. Find the value of θ.

Initially, we have $\cos^{- 1}$ and the bounds of cosfunction are going to be in the interval $[0, π]$ . It represents the range of role="math" localid="1646415761203" $\cos^{- 1}$ .

By using the unit circle, we can say that $θ$ must be equal to $\frac{π}{3}$ , so that we can get $\frac{1}{2}$ .

$\cos θ = \frac{1}{2} \cos^{- 1} \frac{1}{2} = \frac{π}{3}$

Step 3. Find the exact value of the expression.

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

By using the unit circle, we know that $\cos (\frac{π}{3}) = \frac{1}{2}$ . Then,

$\sec (\frac{π}{3}) = \frac{1}{\frac{1}{2}} \sec (\frac{π}{3}) = 2$

Therefore, $\sec (\cos^{- 1} \frac{1}{2}) = 2$ .

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

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.

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In Problems 9–36, find the exact value of each expression.seccos-112

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

Calculus

Geometry

Mechanics Maths

Statistics

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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