Chapter 7: Q. 90 (page 465)

In Problems 81–92, use a graphing utility to solve each equation. Express the solution(s) rounded to two decimal places.
$x^{2} = x + 3 \cos (2 x)$

Short Answer

Expert verified

The solution set is $\{- 0.62.0.81\}$

Step by step solution

Step 1. Given Information

In the given problems we have to use a graphing utility to solve each equation and express the solution(s) rounded to two decimal places.

$x^{2} = x + 3 \cos (2 x)$

Step 2. This type of trigonometric equation cannot be solved by previous methods. A graphing utility, though, can be used here.

Each solution of this equation is the x-coordinate of a point of intersection of the graphs of $Y_{1} = x^{2} and Y_{2} = x + 3 \cos (2 x)$ .

Step 3. The graph of the given equation is

Step 4. There are three points of intersection; the x-coordinates are the solutions that we seek.

Using INTERSECT, we find

$x = - 0.62 x = 0.81$

The solution set is $\{- 0.62.0.81\}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In Problems 81–92, use a graphing utility to solve each equation. Express the solution(s) rounded to two decimal places.
$x^{2} = x + 3 \cos (2 x)$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. This type of trigonometric equation cannot be solved by previous methods. A graphing utility, though, can be used here.

Step 3. The graph of the given equation is

Step 4. There are three points of intersection; the x-coordinates are the solutions that we seek.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Theoretical and Mathematical Physics

Probability and Statistics

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

In Problems 81–92, use a graphing utility to solve each equation. Express the solution(s) rounded to two decimal places.x2=x+3cos(2x)

Short Answer

Step by step solution

Step 1. Given Information

Step 2. This type of trigonometric equation cannot be solved by previous methods. A graphing utility, though, can be used here.

Step 3. The graph of the given equation is

Step 4. There are three points of intersection; the x-coordinates are the solutions that we seek.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Theoretical and Mathematical Physics

Probability and Statistics

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

In Problems 81–92, use a graphing utility to solve each equation. Express the solution(s) rounded to two decimal places.
$x^{2} = x + 3 \cos (2 x)$