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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Limits
When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…
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Question
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Chapter 5.5, Problem 34E
To determine

To write:The function f(x)=sin3x with the help of power reducing formula and graph the function.

Expert Solution & Answer
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Answer to Problem 34E

The function f(x)=sin3x can be rewritten as 12(sinx−sinxcos2x) with the help of power reducing formula. The graph of function f(x) is shown in the figure (1).

Explanation of Solution

Given information:

The function is given as f(x)=sin3x .

Formula used:

Use the power reducing formula sin2x=1−cos2x2 .

Calculation:

As per power reducing formula.

  sin2x=1−cos2x2

Substitute the value in the expression.

  sin3x=sinx(sin2x)=sinx(1−cos2x2)=12(sinx−sinxcos2x)

Therefore the function f(x)=sin3x can be rewritten as 12(sinx−sinxcos2x) .

Draw the graph for the expression 12(sinx−sinxcos2x) as shown in the figure (1).

  Precalculus with Limits: A Graphing Approach, Chapter 5.5, Problem 34E

Figure (1)

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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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