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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. 17 (page 465)

In Problems 11鈥�34, solve each equation on the interval $0 鈮� 胃鈮� 2 蟺$
$\sin (3 胃) = - 1$

Short Answer

Expert verified

The solution set is $\{\frac{蟺}{2}, \frac{7 蟺}{3}, \frac{11 蟺}{3}\}$ .

Step by step solution

01

Step 1. Given Information

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

$\sin (3 胃) = - 1$

02

Step 2. In the interval [0,2π), the sine function equals -1 at 3π2.

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

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

$3 胃 = \frac{3 蟺}{2} + 2 蟺苍$

Divide by 3 on both side

localid="1646585218967" $\frac{3}{3} 胃 = \frac{1}{3} (\frac{3 蟺}{2} + 2 蟺苍) 胃 = \frac{1}{3} 路 \frac{3 蟺}{2} + 2 蟺苍路 \frac{1}{3} 胃 = \frac{蟺}{2} + \frac{2 蟺苍}{3}$

03

Step 3. The general formula is θ=π2+2πn3

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

$胃 = \frac{蟺}{2} + \frac{2 蟺苍}{3}$

localid="1646586125845" role="math" $胃 = \frac{蟺}{2} + \frac{2 蟺脳 0}{3} 胃 = \frac{蟺}{2} + \frac{2 蟺脳 1}{3} 胃 = \frac{蟺}{2} + \frac{2 蟺脳 2}{3} 胃 = \frac{蟺}{2} + \frac{0}{3} 胃 = \frac{3 蟺 + 4 蟺}{3} 胃 = \frac{3 蟺 + 8 蟺}{3} 胃 = \frac{蟺}{2} 胃 = \frac{7 蟺}{3} 胃 = \frac{11 蟺}{3}$

So the solution set islocalid="1646586141392" $\{\frac{蟺}{2}, \frac{7 蟺}{3}, \frac{11 蟺}{3}\}$

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Most popular questions from this chapter

Establish each identity.

$\frac{{(s e c v - \tan v)}^{2} + 1}{c s c v (s e c v - \tan v)} = 2 \tan v$

$\tan^{2} (胃) - \sec^{2} (胃)$

In Problems 9鈥�36, find the exact value of each expression.

$\sin (\cos^{- 1} \frac{1}{2})$

True or False

$\tan (2 胃) = \frac{2 \tan 胃}{1 - \tan^{2} 胃}$

If $z = \tan \frac{伪}{2}$ , show that localid="1646416257885" $\cos 伪 = \frac{1 - z^{2}}{1 + z^{2}}$ .

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