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 37E
To determine

To write:The expression cos4x in first power of cosine and verify both the expressions by graphing utility.

Expert Solution & Answer
Check Mark

Answer to Problem 37E

The expression cos4x can be written as 18(3+4cos2x+cos4x) as a single power of cosine.

Explanation of Solution

Given information:

The expression is given as cos4x .

Formula used:

Use the power reducing formula cos2x=1+cos2x2 .

Calculation:

As per power reducing formula.

  cos2x=1+cos2x2

Substitute the value in the above expression.

  cos4x=(cos2x)2=(1+cos2x2)2=14(1+2cos2x+cos22x)

Further simplify,

  cos4x=14(1+2cos2x+1+cos4x2)=18(2+4cos2x+1+cos4x)=18(3+4cos2x+cos4x)

Therefore the expression cos4x can be written as 18(3+4cos2x+cos4x) as a single power of cosine.

Verify both the expressions using graphical utility:

Draw the graph for the expression cos4x as shown in the Figure (1).

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 5.5, Problem 37E , additional homework tip 1

Figure (1)

Draw the graph for the expression 18(3+4cos2x+cos4x) as shown in the Figure (2).

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 5.5, Problem 37E , additional homework tip 2

Figure (2)

As both the expressions shows same values in Figure (1) and Figure (2) at each point.

Therefore both the expressions cos4x and 18(3+4cos2x+cos4x) are same.

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Chapter 5.5, Problem 36E
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Chapter 5.5, Problem 38E

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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