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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Question
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Chapter 5.4, Problem 93E
To determine

To find:The angle between the given pair of lines y=x, y=3x .

Expert Solution & Answer
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Answer to Problem 93E

The angle between the given pair of lines y=x, y=3x is 15° .

Explanation of Solution

Given information:

The given two lines are y1=m1x+b1, and y2=m2x+b2 .

Calculation:

Let the graph for the two lines is y1=m1x+b1 and y2=m2x+b2 .

  Precalculus with Limits: A Graphing Approach, Chapter 5.4, Problem 93E

Let the angle made by y1=m1x+b1 with the x -axis be θ1 and y2=m2x+b2 with the x -axis be θ2 .

  tanθ1=m1,tanθ2=m2, and ​θ=θ1−θ2

Take tangent on both sides in equation θ=θ1−θ2 .

  tanθ=tan(θ1−θ2)tanθ=tanθ1−tanθ21+tanθ1tanθ2tanθ=m1−m21+m1m2​

Th above equation is the formulae for the angle between two lines with slopes m1 and m2 , (m1<m2) .

Given lines are y=x with slope 1 , and y=3x with slope 3 .

  m1=3 and m2=1       (since m1>m2)

Calculate the angle.

  tanθ=m1−m21+m1m2​tanθ=3−11+3(1)​tanθ=tan15°θ=15°

Therefore, the angle between the given pair of lines y=x, y=3x is 15° .

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Chapter 5.4, Problem 92E
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Chapter 5.4, Problem 94E

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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