Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Question
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Chapter 5.4, Problem 78E

(a)

To determine

Thegraph for the model.

(a)

Expert Solution
Check Mark

Answer to Problem 78E

The graph for the model is shown in figure (1).

Explanation of Solution

Given information:

The motion of the model is given by equation.

  y=13sin2t+14cos2t

Calculation:

The graph for the model is shown in figure (1).

  Precalculus with Limits: A Graphing Approach, Chapter 5.4, Problem 78E , additional homework tip 1

Figure (1)

Therefore, the graph for the model is shown in figure (1).

(b)

To determine

Thegraph for the given identity and verify the answer.

(b)

Expert Solution
Check Mark

Answer to Problem 78E

It can be easily verified from the graph in part (a) and (b) that the result in both are same.

Explanation of Solution

Given information:

The given identity is y=a2+b2sin(Bt+C) .

Calculation:

The motion of the model is given by equation.

  y=13sin2t+14cos2t

The given identity is y=a2+b2sin(Bt+C) .

Where a=13,b=14,B=2,C=arctan(1/41/3)=arctan(13)=0.643501

So, y=0.41667sin(2t+0.64350) .

  Precalculus with Limits: A Graphing Approach, Chapter 5.4, Problem 78E , additional homework tip 2

From the graph it can be easily verified from the graph in part (a) and (b) that the both are same.

Therefore,it can be easily verified from the graph in part (a) and (b) that the result in both are same.

(c)

To determine

Theamplitude of the oscillations of the weight.

(c)

Expert Solution
Check Mark

Answer to Problem 78E

The amplitude of the oscillations of the weight is 0.41667 .

Explanation of Solution

Given information:

The motion of the model is given by equation.

  y=13sin2t+14cos2t

Calculation:

The amplitude of the oscillations of the weight.

  a2+b2=0.41667

Therefore, the amplitude of the oscillations of the weight is 0.41667 .

(d)

To determine

Thefrequency of the oscillations of the weight.

(d)

Expert Solution
Check Mark

Answer to Problem 78E

The frequency of the oscillations of the weight is B=2 .

Explanation of Solution

Given information:

The motion of the model is given by equation.

  y=13sin2t+14cos2t

Calculation:

The frequency of the oscillations of the weight.

  B=2

Therefore, the frequency of the oscillations of the weight is B=2 .

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Chapter 5.4, Problem 77E
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Chapter 5.4, Problem 79E

Chapter 5 Solutions

Precalculus with Limits: A Graphing Approach

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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