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 5.3, Problem 90E

a.

To determine

To graph: The given function in the given interval and approximate maximum and minimum points (to four decimal places) of the graph.

a.

Expert Solution
Check Mark

Answer to Problem 90E

The approximate maximum and minimum points are:

Maxima: (3.6652,1.25),(5.7596,1.25)

Minima: (1.5708,−1),(4.7124,1)

Explanation of Solution

Given information:

The following function:

  f(x)=cos2x−sinx

The following interval:

  [0,2π)

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 cos2x−sinx 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 5.3, Problem 90E , additional homework tip 1

Interpretation:

Using TRACE feature on the calculator, the maximum and minimum points are obtained as:

Maxima: (3.6652,1.25),(5.7596,1.25)

Minima: (1.5708,−1),(4.7124,1)

b.

To determine

To solve: The given trigonometric equation and verify that the x-coordinates of the maximum and minimum points of f are among its solutions.

b.

Expert Solution
Check Mark

Answer to Problem 90E

The solutionsof the trigonometric equation are:

  x=π2+2nπx=3π2+2nπx=7π6+2nπx=11π6+2nπ

Explanation of Solution

Given information:

The following equation:

  −2sinxcosx−cosx=0

Calculation:

The given equation is solved as:

  −2sinxcosx−cosx=0           [Given]       cosx(−2sinx−1)=0               [Factor]cosx=0                                   [Set each factor as 0]x=π2+2nπ,3π2+2nπ               [Using inverse trigonometric function]sinx=−12x=7π6+2nπ,11π6+2nπ           [Using inverse trigonometric function]

To verify if the x-coordinates of the maximum and minimum points of f are among the solutions of the trigonometric equation, graph both equations in the same window as follows:

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 expressions Y1=cos2x−sinx and Y2=−2sinxcosx−cosx 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 5.3, Problem 90E , additional homework tip 2

Interpretation:

The x-coordinates of the trigonometric function( −2sinxcosx−cosx ) at 0 is same as the x-coordinates of the maximum and the minimum points of f(x) . Hence, verified.

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Chapter 5.3, Problem 89E
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Chapter 5.3, Problem 91E

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
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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01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
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