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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Question
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Chapter 5.5, Problem 93E
To determine

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

Expert Solution & Answer
Check Mark

Answer to Problem 93E

The solution of the given equation in the interval [0,2π) is x=π6,5π6 .

Explanation of Solution

Given information:

The following equation:

  cos2xsin3xsinx1=0

The following interval:

  [0,2π)

Formula used:

The following sum to product formula:

  sinusinv=2cos(u+v2)sin(uv2)

Calculation:

The given equation can be solved as follows:

   cos2xsin3xsinx1=0                                      [Given] cos2xsin3xsinx=1                                           [Add 1 to both sides]    cos2x2cos(3x+x2)sin(3xx2)=1                     [Sum to product formula]      cos2x2cos(4x2)sin(2x2)=1                                [Add and subtract]    cos2x2cos2xsinx=1                                            [Simplify]12sinx=1                                                      [Divide common factors]2sinx=1                                                      [Multiply both sides by 2sinxsinx=12                                                       [Divide both sides by 2]x=arcsin12                                                  [Inverse trigonometric function]x=π6,5π6                                                     [Value of inverse]

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 cos2xsin3xsinx1 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 93E

Interpretation:

In the interval [0,2π) , the value of the equation is 0 at x=π6,5π6 . Hence, verified.

Chapter 5 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - Prob. 37ECh. 5.1 - Prob. 38ECh. 5.1 - Prob. 39ECh. 5.1 - Prob. 40ECh. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - Prob. 53ECh. 5.1 - Prob. 54ECh. 5.1 - Prob. 55ECh. 5.1 - Prob. 56ECh. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.1 - Prob. 59ECh. 5.1 - Prob. 60ECh. 5.1 - Prob. 61ECh. 5.1 - Prob. 62ECh. 5.1 - Prob. 63ECh. 5.1 - 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