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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. 64 (page 451)

Find the exact solution of each equation:
$- 6 \sin^{- 1} (3 x) = 蟺$ .

Short Answer

Expert verified

The exact solution of the equation $- 6 \sin^{- 1} (3 x) = 蟺$ isrole="math" localid="1647543569015" ${- \frac{1}{6}}$ .

Step by step solution

01

Step 1. Given Information.

The trigonometric equation is,

$- 6 \sin^{- 1} (3 x) = 蟺$ .

02

Step 2. Finding the value.

The equation is,

$- 6 \sin^{- 1} (3 x) = 蟺$

Dividing both sides by $- 6$ ,

$\frac{- 6 \sin^{- 1} (3 x)}{- 6} = \frac{蟺}{- 6} 鈬� \sin^{- 1} (3 x) = - \frac{蟺}{6}$

The equation can be rewritten as,

$3 x = \sin (- \frac{蟺}{6}) 鈬� 3 x = - \sin (\frac{蟺}{6}) 鈬� 3 x = - \frac{1}{2} 鈬� x = - \frac{1}{6}$

The solution set is ${- \frac{1}{6}}$ .

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