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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. 85 (page 505)

Use a graphing utility to solve the equation on the interval $0 鈮� x 鈮� 2 蟺$ . Approximate any solutions rounded to two decimal places.
$2 \cos^{- 1} x + 蟺 = 4 \cos^{- 1} x$

Short Answer

Expert verified

The exact solution of the equation is $\{0\}$ .

Step by step solution

01

Step 1. Given information.

Consider the given question,

$2 \cos^{- 1} x + 蟺 = 4 \cos^{- 1} x$

Subtract $2 \cos^{- 1} x$ from both sides,

$2 \cos^{- 1} x + 蟺 - 2 \cos^{- 1} x = 4 \cos^{- 1} x - 2 \cos^{- 1} x 蟺 = 4 \cos^{- 1} x - 2 \cos^{- 1} x 蟺 = 2 \cos^{- 1} x$

Divide both sides by $2$ ,

$\frac{蟺}{2} = \frac{2 \cos^{- 1} x}{2} \frac{蟺}{2} = \cos^{- 1} x$

02

Step 2. Rewrite the equation.

As $y = \sin^{- 1} x$ means $x = \sin y$ , where,

$- \frac{蟺}{2} 鈮� 胃鈮� \frac{蟺}{2}$

On rewriting the equation, we get,

localid="1646497927832" $x = \cos (\frac{蟺}{2}) x = 0$

Therefore, the solution set is ${0}$

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