Q. 41 In Problems 35鈥� 44, 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. 41 (page 465)

In Problems 35鈥� 44, solve each equation. Give a general formula for all the solutions. List six solutions.
$\cos (2 胃) = - \frac{1}{2}$

Short Answer

Expert verified

A general formula for all the solutions is $\{胃 | 胃 = \frac{2 蟺 + 6 苍蟺}{6} \frac{4 蟺 + 6 苍蟺}{6}\}$ and list of six solution of the given equation is $\{\frac{4 蟺}{3}, \frac{5 蟺}{3}, \frac{7 蟺}{3}, \frac{8 蟺}{3}, \frac{10 蟺}{3}, \frac{11 蟺}{3}\}$ .

Step by step solution

Step 1. Given Information

In the given problems we have to solve each equation. Give a general formula for all the solutions. List six solutions.

$\cos (2 胃) = - \frac{1}{2}$

Step 2. The period of the cosine function is 2π.

In the interval $[0, 2 蟺)$ , the cosine function equals $- \frac{1}{2}$ at $\frac{2 蟺}{3} and \frac{4 蟺}{3}$ .

$2 胃 = \frac{2 蟺}{3} + 2 苍蟺 or 2 胃 = \frac{4 蟺}{3} + 2 苍蟺 2 胃 = \frac{2 蟺 + 6 苍蟺}{3} or 2 胃 = \frac{4 蟺 + 6 苍蟺}{3} \frac{2}{2} 胃 = \frac{2 蟺 + 6 苍蟺}{3} 路 \frac{1}{2} or 2 胃 = \frac{4 蟺 + 6 苍蟺}{3} 路 \frac{1}{2} 胃 = \frac{2 蟺 + 6 苍蟺}{6} or 胃 = \frac{4 蟺 + 6 苍蟺}{6}$

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

$胃 = \frac{2 蟺 + 6 苍蟺}{6} or 胃 = \frac{2 蟺 + 6 苍蟺}{6}$

Step 3. The general formula is θ=2π+6nπ6 or θ=4π+6nπ6

We find the six solutions by putting $n = 1, 2, 3, . . . . . . . .$ in general formula

Six of the solutions are

$\{\frac{8 蟺}{6}, \frac{10 蟺}{6}, \frac{14 蟺}{6}, \frac{16 蟺}{6}, \frac{20 蟺}{6}, \frac{22 蟺}{6}\} \{\frac{4 蟺}{3}, \frac{5 蟺}{3}, \frac{7 蟺}{3}, \frac{8 蟺}{3}, \frac{10 蟺}{3}, \frac{11 蟺}{3}\}$

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91影视

In Problems 35鈥� 44, solve each equation. Give a general formula for all the solutions. List six solutions.
$\cos (2 胃) = - \frac{1}{2}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. The period of the cosine function is 2π.

Step 3. The general formula is θ=2π+6nπ6 or θ=4π+6nπ6

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91影视

In Problems 35鈥� 44, solve each equation. Give a general formula for all the solutions. List six solutions.cos(2胃)=-12

Short Answer

Step by step solution

Step 1. Given Information

Step 2. The period of the cosine function is 2π.

Step 3. The general formula is θ=2π+6nπ6 or θ=4π+6nπ6

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Statistics

Logic and Functions

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

In Problems 35鈥� 44, solve each equation. Give a general formula for all the solutions. List six solutions.
$\cos (2 胃) = - \frac{1}{2}$