PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Chapter 5.5, Problem 70E
To determine

To find: The solutions of the given equation in the given interval.

Expert Solution & Answer
Check Mark

Answer to Problem 70E

The solutions of the given equation in the interval [0,2π) are x=0,π2,3π2 .

Explanation of Solution

Given information:

The following equation:

  tanx2−sinx=0

The following interval:

  [0,2π)

Formula used:

The following half angle formula

  tanu2=1−cosusinu

The following Pythagorean relation:

  sin2x+cos2x=1

Calculation:

The given equation can be solved as follows:

  tanx2−sinx=0                           [Given]1−cosxsinx−sinx=0                      [Half angle formula]1−cos−sin2xsinx=0                       [Subtract fractions]cos2x−cosxsinx=0                        [Pythagorean identity]cos2x−cosx=0                         [Multiply both sides by sinx]cosx(cosx−1)=0                       [Factor]cosx=0       cosx−1=0            [Set each factor to 0]cosx=0          cosx=1               [Simplify]x=arccos(0)       x=arccos(1)     [Inverse trigonometric function]x=π2,3π2           x=0,2π            [Find value of inverse]

Among all the solutions of x , x=0,π2,3π2 lie in the given interval. The solution is verified graphically as:

Graph:

Sketch the graph using graphing utility.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press Y= button.

Step 3: Enter the expression tanx2−sinx and which is required to graph.

Step 4: Press GRAPH button to graph the function.

The graph is obtained as:

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 5.5, Problem 70E

Interpretation:

In the interval [0,2π) , the value of the equation is 0 at x=0,π2,3π2 . Hence, verified.

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Chapter 5.5, Problem 69E
Next
Chapter 5.5, Problem 71E

Chapter 5 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
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