Chapter 7: Q. 16 (page 465)

In Problems 11–34, solve each equation on the interval $0 \leq θ \leq 2 π$
$4 \cos^{2} θ - 3 = 0$

Short Answer

Expert verified

The solution set is $\{\frac{π}{6}, \frac{5 π}{6}, \frac{7 π}{6} \frac{11 π}{6}\}$ .

Step by step solution

Step 1. Given Information

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

$4 \cos^{2} θ - 3 = 0$

Step 2. Firstly solving the equation

Add 3 on both side

$4 \cos^{2} θ - 3 + 3 = 0 + 3 4 \cos^{2} θ = 3$

Divide by 4 on both side

$\frac{4}{4} \cos^{2} θ = \frac{3}{4} \cos^{2} θ = \frac{3}{4}$

Taking square root on both side

$\cos θ = \pm \sqrt{\frac{3}{4}} \cos θ = \pm \frac{\sqrt{3}}{2}$

$\cos θ = \frac{\sqrt{3}}{2} and \cos θ = - \frac{\sqrt{3}}{2}$

Step 3. After solving the equation cosθ=32 and cosθ=-32

The period of the cosine function is $2 π$ . In the interval $[0, 2 π)$ , there are two angles $θ$ for which

$\cos θ = \frac{\sqrt{3}}{2} : θ = \frac{π}{6} and θ = \frac{11 π}{6}$

Step 4. The period of the cosine function cosθ=-32 is 2π.

The period of the cosine function is $2 π$ . In the interval $[0, 2 π)$ , there are two angles $θ$ for which role="math" localid="1646583425702" $\cos θ = - \frac{\sqrt{3}}{2} : θ = \frac{5 π}{6} and θ = \frac{7 π}{6}$

The solution set is $\{\frac{π}{6}, \frac{5 π}{6}, \frac{7 π}{6} \frac{11 π}{6}\}$ .

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In Problems 11–34, solve each equation on the interval $0 \leq θ \leq 2 π$
$4 \cos^{2} θ - 3 = 0$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Firstly solving the equation

Step 3. After solving the equation cosθ=32 and cosθ=-32

Step 4. The period of the cosine function cosθ=-32 is 2π.

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In Problems 11–34, solve each equation on the interval 0≤θ≤2π4cos2θ-3=0

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Firstly solving the equation

Step 3. After solving the equation cosθ=32 and cosθ=-32

Step 4. The period of the cosine function cosθ=-32 is 2π.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Discrete Mathematics

Logic and Functions

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

In Problems 11–34, solve each equation on the interval $0 \leq θ \leq 2 π$
$4 \cos^{2} θ - 3 = 0$