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 18E
To determine

To calculate:Thesolution of the equation (sin2x+cos2x)2=1 in the interval [0,2π) .

Expert Solution & Answer
Check Mark

Answer to Problem 18E

The solution set of the equation (sin2x+cos2x)2=1 in the interval [0,2π) is {0,π4,π2,3π4,π,5π4,3π2,7π4} .

Explanation of Solution

Given information:

The given equation is (sin2x+cos2x)2=1 .

Formula used:

Use the formula.

  (a+b)2=a2+b2+2ab

Calculation:

Substitute the value sin2x for a and cos2x for b in the equation.

  sin22x+cos22x+2sin2xcos2x=11+2sin2xcos2x=12sin2xcos2x=0

The solutions in the interval [0,2π) , substitute the factor 2sin2x=0 .

  x=0,π2,π,3π2

The solutions in the interval [0,2π) , substitute the factor cos2x=0 .

  x=π4,3π4,5π4,7π4

Therefore, the solution set is

  {0,π2,π,3π2}{π4,3π4,5π4,7π4}={0,π4,π2,3π4,π,5π4,3π2,7π4}

Verify the solutions using graphical utility:

Draw the graph for the equation (sin2x+cos2x)2=1 as shown in Figure(1).

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 5.5, Problem 18E

Figure(1)

From the above, it is clear that {0,π4,π2,3π4,π,5π4,3π2,7π4} are the solutions.

Therefore, the solution of the equation (sin2x+cos2x)2=1 in the interval [0,2π){0,π4,π2,3π4,π,5π4,3π2,7π4} .

Chapter 5 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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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