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 5.5, Problem 39E
To determine

To write:The expression sin2xcos4x in first power of cosine and verify both the expressions by graphing utility.

Expert Solution & Answer
Check Mark

Answer to Problem 39E

The expression sin2xcos4x can be written as 116(1+cos2x−cos4x−cos2xcos4x) as a single power of cosine.

Explanation of Solution

Given information:

The expression is given as sin2xcos4x .

Formula used:

Use the power reducing formula

  cos2x=1+cos2x2 and sin2x=1−cos2x2 .

Calculation:

As per power reducing formula.

  cos2x=1+cos2x2 and sin2x=1−cos2x2

Substitute the value in the above expression.

  sin2xcos4x=(1−cos2x2)(1+cos2x2)(1+cos2x2)=18(1−cos22x)(1+cos2x)=18(1−1+cos4x2)(1+cos2x)

Simplify further,

sin2xcos4x=18(1−cos4x2)(1+cos2x)=116(1+cos2x−cos4x−cos4xcos2x)

Therefore the expression sin2xcos4x can be written as 116(1+cos2x−cos4x−cos2xcos4x) as a single power of cosine.

Verify both the expressions using graphical utility:

Draw the graph for the expression sin2xcos4x as shown in the Figure (1).

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 5.5, Problem 39E , additional homework tip 1

Figure (1)

Draw the graph for the expression 116(1+cos2x−cos4x−cos2xcos4x) as shown in the Figure (2).

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 5.5, Problem 39E , 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 sin2xcos4x and 116(1+cos2x−cos4x−cos2xcos4x) are same.

Previous
Chapter 5.5, Problem 38E
Next
Chapter 5.5, Problem 40E

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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Prob. 34ECh. 5.4 - Prob. 35ECh. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Prob. 40ECh. 5.4 - Prob. 41ECh. 5.4 - Prob. 42ECh. 5.4 - Prob. 43ECh. 5.4 - Prob. 44ECh. 5.4 - Prob. 45ECh. 5.4 - Prob. 46ECh. 5.4 - Prob. 47ECh. 5.4 - Prob. 48ECh. 5.4 - Prob. 49ECh. 5.4 - Prob. 50ECh. 5.4 - Prob. 51ECh. 5.4 - Prob. 52ECh. 5.4 - Prob. 53ECh. 5.4 - Prob. 54ECh. 5.4 - Prob. 55ECh. 5.4 - Prob. 56ECh. 5.4 - Prob. 57ECh. 5.4 - Prob. 58ECh. 5.4 - Prob. 59ECh. 5.4 - Prob. 60ECh. 5.4 - Prob. 61ECh. 5.4 - Prob. 62ECh. 5.4 - Prob. 63ECh. 5.4 - Prob. 64ECh. 5.4 - Prob. 65ECh. 5.4 - Prob. 66ECh. 5.4 - Prob. 67ECh. 5.4 - Prob. 68ECh. 5.4 - Prob. 69ECh. 5.4 - Prob. 70ECh. 5.4 - Prob. 71ECh. 5.4 - Prob. 72ECh. 5.4 - Prob. 73ECh. 5.4 - Prob. 74ECh. 5.4 - Prob. 75ECh. 5.4 - Prob. 76ECh. 5.4 - Prob. 77ECh. 5.4 - Prob. 78ECh. 5.4 - Prob. 79ECh. 5.4 - Prob. 80ECh. 5.4 - Prob. 81ECh. 5.4 - Prob. 82ECh. 5.4 - Prob. 83ECh. 5.4 - Prob. 84ECh. 5.4 - Prob. 85ECh. 5.4 - Prob. 86ECh. 5.4 - 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Double and Half Angle Formulas | Analytic Trig | Pre-Calculus; Author: Brian McLogan;https://www.youtube.com/watch?v=eTdKgsyCmHs;License: Standard YouTube License, CC-BY