Chapter 7: Q. 85 (page 505)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

Consider the given question,

$2 \cos^{- 1} x + π = 4 \cos^{- 1} x$

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

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

Divide both sides by $2$ ,

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

Step 2. Rewrite the equation.

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

$- \frac{π}{2} \leq θ \leq \frac{π}{2}$

On rewriting the equation, we get,

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

Therefore, the solution set is ${0}$

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Rewrite the equation.

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Use a graphing utility to solve the equation on the interval 0≤x≤2π. Approximate any solutions rounded to two decimal places.2cos-1x+π=4cos-1x

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Rewrite the equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Study anywhere. Anytime. Across all devices.

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