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 47E
To determine

To find: the exact value of the trigonometric expression when sinu=−725 and cosv=−45 .

Expert Solution & Answer
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Answer to Problem 47E

  tan(u+v)=43 .

Explanation of Solution

Given information:

Given expression,

  tan(u+v)

Calculation:

Consider that sinu=−725 and cosv=−45 , u and v are in quadrant III.

The sine of an angle is equal to opposite side over the hypotenuse. Since sinu=−725 and u is quadrant III. So, the following figure will obtain:

  Precalculus with Limits: A Graphing Approach, Chapter 5.4, Problem 47E , additional homework tip 1

Since cosine of an angle is equal to adjacent side over the hypotenuse and u is in quadrant III.

Therefore:

  tanu=724

Since, cosv=−45 and v is in quadrant III. Consider the following figure:

  Precalculus with Limits: A Graphing Approach, Chapter 5.4, Problem 47E , additional homework tip 2

Since the side of an angle is equal to opposite side over the hypotenuse. Therefore:

  tanv=34

Apply the sum formula for tangent that is:

  tan(u+v)=tanu+tanv1−tanutanv

Substitute:

  tanu=724,tanv=34

So,

  tan(u+v)=(724)+(34)1−(724)(34)=(7+1824)1−(2196)=(2524)1−(2196)=(2524)(7596)=2524(9675)=43

Therefore,

  tan(u+v)=43 .

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Chapter 5.4, Problem 46E
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Chapter 5.4, Problem 48E

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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