Chapter 7: Q. 12 (page 465)

In Problems 11–34, solve each equation on the interval $0 \leq θ \leq 2 π$ .
$1 - \cos θ = \frac{1}{2}$

Short Answer

Expert verified

The solution set is $\{\frac{π}{3}, \frac{5 π}{3}\}$

Step by step solution

Step 1. Given Information

In the given problem we have to solve each equation on the interval $0 \leq θ \leq 2 π$ .

$1 - \cos θ = \frac{1}{2}$

Step 2. Firstly solving the equation 1-cosθ=12

Subtract 1 on both side

$1 - \cos θ - 1 = \frac{1}{2} - 1 - \cos θ = \frac{1}{2} - 1 \cdot \frac{2}{2} - \cos θ = \frac{1}{2} - \frac{2}{2} - \cos θ = \frac{1 - 2}{2} - \cos θ = \frac{- 1}{2}$

Multiply with $- 1$ on both side

role="math" localid="1646565140078" $- \cos θ \times (- 1) = \frac{- 1}{2} \times (- 1) \cos θ = \frac{1}{2}$

Step 3. After solving the equation cosθ=12

The period of the cosine function is $2 π$ . In the interval $[0, 2 π)$ , there are two angles $θ$ for whichlocalid="1646566828893" $\cos θ = \frac{1}{2} : θ = \frac{π}{3} and θ = \frac{5 π}{3}$

So the solutions set is $\frac{π}{3}, \frac{5 π}{3}$

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In Problems 11–34, solve each equation on the interval $0 \leq θ \leq 2 π$ .
$1 - \cos θ = \frac{1}{2}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Firstly solving the equation 1-cosθ=12

Step 3. After solving the equation cosθ=12

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In Problems 11–34, solve each equation on the interval 0≤θ≤2π.1-cosθ=12

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Firstly solving the equation 1-cosθ=12

Step 3. After solving the equation cosθ=12

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Problems 11–34, solve each equation on the interval $0 \leq θ \leq 2 π$ .
$1 - \cos θ = \frac{1}{2}$