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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Chapter 5.5, Problem 19E
To determine

To calculate:Thesolution of the equation tan2x−cotx=0 in the interval [0,2π) .

Expert Solution & Answer
Check Mark

Answer to Problem 19E

The solution set of the equation tan2x−cotx=0 in the interval [0,2π) is {π6,π2,5π6,7π6,3π2,11π6} .

Explanation of Solution

Given information:

The given equation is tan2x−cotx=0 .

Formula used:

Use the double angle formula.

  tan2x=2tanx1−tan2x

Calculation:

Substitute the value of tan2x in the given equation.

  2tanx1−tan2x−cotx=0

Further simplify.

  tan2x−cotx=0tan2x−1tanx=0cotx(tan2xtanx−1)=0 .

Further simplify.

  cotx(2tan2x1−tan2x−1)=0cotx(2tan2x−1+tan2x1−tan2x)=0cotx(3tan2x−11−tan2x)=0cotx(3tan2x−1)=0

The solutions in the interval [0,2π) , substitute the factor 3tan2x−1=0 .

  x=π6,5π6,7π6,11π6

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

  x=π6,π2,5π6,7π6,3π2,11π6

Therefore, the solution set is

  {π6,5π6,7π6,11π6}∪{π6,π2,5π6,7π6,3π2,11π6}={π6,π2,5π6,7π6,3π2,11π6}

Verify the solutions using graphical utility:

Draw the graph for the equation tan2x−cotx=0 as shown in Figure(1).

  Precalculus with Limits: A Graphing Approach, Chapter 5.5, Problem 19E

Figure(1)

From the above, it is clear that {π6,π2,5π6,7π6,3π2,11π6} are the solutions.

Therefore, the solution of the equation tan2x−cotx=0 in the interval [0,2π){π6,π2,5π6,7π6,3π2,11π6} .

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Chapter 5.5, Problem 18E
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Chapter 5.5, Problem 20E

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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Find the solutions to a trig equation between 0 and 2pi; Author: Brian McLogan;https://www.youtube.com/watch?v=h7trDHjKCYc;License: Standard YouTube License, CC-BY