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 44E
To determine

To find: the exact value of the trigonometric expression when sinu=513 and cosv=−35 .

Expert Solution & Answer
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Answer to Problem 44E

  tan(u+v)=−6316 .

Explanation of Solution

Given information:

Given expression,

  tan(u+v) .

Calculation:

Consider that sinu=513 and cosv=−35 , u and v are in quadrant II.

The sine of an angle is equal to opposite side over the hypotenuse. Since sinu=513 and u is quadrant II. So, the following figure will obtain:

  Precalculus with Limits: A Graphing Approach, Chapter 5.4, Problem 44E , additional homework tip 1

Since tangentof an angle is equal to opposite side to the adjacent side.

Therefore:

  tanu=5−12=−512

Since, cosv=−35 and v is in quadrant II. Consider the following figure:

  Precalculus with Limits: A Graphing Approach, Chapter 5.4, Problem 44E , additional homework tip 2

The tangent of an angle is equal to opposite side to the adjacent side therefore:

  tanv=4−3=−43

Apply the sum formula for tangent that is:

  tan(u+v)=tanu+tanv1−tanutanv

Substitute:

  tanu=512,tanv=−43

So,

  tan(u+v)=(−512)+(−43)1−(−512)(−43)=(−5−1612)1−(−512)(−43)=(−2112)1−(59)=(−2112)(49)=−2112(94)=−6316

Therefore,

  tan(u+v)=−6316 .

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Chapter 5.4, Problem 43E
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Chapter 5.4, Problem 45E

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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