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+tanv1tanutanv

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 .

Chapter 5 Solutions

Precalculus with Limits: A Graphing Approach

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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