Q. 19 In Problems 11鈥�34, solve each ... [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 465)

In Problems 11鈥�34, solve each equation on the interval $0 鈮� 胃鈮� 2 蟺$ .
$\cos (2 胃) = - \frac{1}{2}$

Short Answer

Expert verified

The solution set is $\{\frac{蟺}{3}, \frac{2 蟺}{3}, \frac{4 蟺}{3}, \frac{5 蟺}{3}\}$ .

Step by step solution

Step 1. Given Information

In the given problem we have to solve each equation on the interval $0 鈮� 胃鈮� 2 蟺$

$\cos (2 胃) = - \frac{1}{2}$

Step 2. In the interval [0,2π), the cosine function equals -12 at 2π3.

So, we know that $2 胃$ must equal $\frac{2 蟺}{3}$ .

To find these solutions, write the general formula that gives all the solutions.

localid="1646587269475" $2 胃 = \frac{2 蟺}{3} + 2 蟺苍$

Divide by 2 on both side

localid="1646592113006" $\frac{2}{2} 胃 = \frac{1}{2} (\frac{2 蟺}{3} + 2 蟺苍) 胃 = \frac{1}{2} 脳 \frac{2 蟺}{3} + 2 蟺苍脳 \frac{1}{2} 胃 = \frac{蟺}{3} + 蟺苍$

$胃 = \frac{2 蟺}{3} + 蟺苍$

Step 3. The general formula is θ=π3+πn,θ=2π3+πn

So the value of given function in interval $[0, 2 蟺)$ is

localid="1646592541288" $胃 = \frac{蟺}{3} + 蟺脳 0 胃 = \frac{蟺}{3} + 蟺脳 1 胃 = \frac{2 蟺}{3} + 蟺脳 0 胃 = \frac{2 蟺}{3} + 蟺脳 1 胃 = \frac{蟺}{3} 胃 = \frac{蟺}{3} + 蟺胃 = \frac{2 蟺}{3} 胃 = \frac{2 蟺}{3} + 蟺胃 = \frac{蟺}{3} 胃 = \frac{蟺 + 3 蟺}{3} 胃 = \frac{2 蟺}{3} 胃 = \frac{2 蟺 + 3 蟺}{3} 胃 = \frac{蟺}{3} 胃 = \frac{4 蟺}{3} 胃 = \frac{2 蟺}{3} 胃 = \frac{5 蟺}{3}$

So the solution set is localid="1646592566280" $\{\frac{蟺}{3}, \frac{2 蟺}{3}, \frac{4 蟺}{3}, \frac{5 蟺}{3}\}$ .

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91影视

In Problems 11鈥�34, solve each equation on the interval $0 鈮� 胃鈮� 2 蟺$ .
$\cos (2 胃) = - \frac{1}{2}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. In the interval [0,2π), the cosine function equals -12 at 2π3.

Step 3. The general formula is θ=π3+πn,θ=2π3+πn

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91影视

In Problems 11鈥�34, solve each equation on the interval 0鈮�胃鈮�2蟺.cos(2胃)=-12

Short Answer

Step by step solution

Step 1. Given Information

Step 2. In the interval [0,2π), the cosine function equals -12 at 2π3.

Step 3. The general formula is θ=π3+πn,θ=2π3+πn

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Problems 11鈥�34, solve each equation on the interval $0 鈮� 胃鈮� 2 蟺$ .
$\cos (2 胃) = - \frac{1}{2}$