Q. 74 In Problems 69-78, solve each eq... [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. 74 (page 496)

In Problems $69 - 78$ , solve each equation on the interval $0 鈮� 胃 < 2 蟺$ .
$\cos (2 胃) + \cos (4 胃) = 0$ .

Short Answer

Expert verified

The solution set for the equation $\cos (2 胃) + \cos (4 胃) = 0$ is, $\{\frac{蟺}{6}, \frac{蟺}{2}, \frac{5 蟺}{6}, \frac{7 蟺}{6}, \frac{3 蟺}{2}, \frac{11 蟺}{6}\}$ .

Step by step solution

Step 1 Given equation is,

$\cos (2 胃) + \cos (4 胃) = 0$ .

The double angle formula for $\cos (2 胃)$ is $\cos (2 胃) = 2 \cos^{2} 胃 - 1$ .

Substitute the known values in the given equation.

$\cos (2 胃) + (2 \cos^{2} (2 胃) - 1) = 0 (2 \cos^{2} 胃 - 1) + (2 \cos^{2} (2 胃) - 1) = 0 (2 \cos^{2} 胃 - 1) + (2 {(2 \cos^{2} 胃 - 1)}^{2} - 1) = 0 (2 \cos^{2} 胃 - 1) + (2 (4 \cos^{4} 胃 - 4 \cos^{2} 胃 + 1) - 1) = 0 (2 \cos^{2} 胃 - 1) + (8 \cos^{4} 胃 - 8 \cos^{2} 胃 + 1) = 0 8 \cos^{4} 胃 - 6 \cos^{2} 胃 = 0 2 \cos^{2} 胃 (4 \cos^{2} 胃 - 3) = 0$

Step 2 Apply the zero product property.

$2 \cos^{2} 胃 = 0 o r (4 \cos^{2} 胃 - 3) = 0 \cos^{2} 胃 = 0 o r 4 \cos^{2} 胃 = 3 \cos 胃 = 0 o r \cos^{2} 胃 = \frac{3}{4} \cos 胃 = 卤 \sqrt{\frac{3}{4}} \cos 胃 = 卤 \frac{\sqrt{3}}{2}$

Solving each equation in the interval $[0, 2 蟺)$ is,

$胃 = \frac{蟺}{2} 胃 = \frac{3 蟺}{2} 胃 = \frac{蟺}{6} 胃 = \frac{11 蟺}{6} 胃 = \frac{5 蟺}{6} 胃 = \frac{7 蟺}{6}$

Therefore, the solution set is, $\{\frac{蟺}{2}, \frac{蟺}{6}, \frac{5 蟺}{6}, \frac{7 蟺}{6}, \frac{3 蟺}{2}, \frac{11 蟺}{6}\}$ .

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91影视

In Problems $69 - 78$ , solve each equation on the interval $0 鈮� 胃 < 2 蟺$ .
$\cos (2 胃) + \cos (4 胃) = 0$ .

Short Answer

Step by step solution

Step 1 Given equation is,

Step 2 Apply the zero product property.

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91影视

In Problems 69-78, solve each equation on the interval 0鈮�胃<2蟺.cos2胃+cos4胃=0.

Short Answer

Step by step solution

Step 1 Given equation is,

Step 2 Apply the zero product property.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Calculus

Mechanics Maths

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Pure Maths

Study anywhere. Anytime. Across all devices.

In Problems $69 - 78$ , solve each equation on the interval $0 鈮� 胃 < 2 蟺$ .
$\cos (2 胃) + \cos (4 胃) = 0$ .