PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Question
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Chapter 5.4, Problem 50E
To determine

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

Expert Solution & Answer
Check Mark

Answer to Problem 50E

  cos(v−u)=117125 .

Explanation of Solution

Given information:

Given expression,

  cos(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 W/LIMITS:GRAPH.APPROACH(HS), Chapter 5.4, Problem 50E , additional homework tip 1

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

Therefore:

  cosu=−2425

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

  PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 5.4, Problem 50E , additional homework tip 2

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

  sinv=−35

Apply the difference formula for cosine that is:

  cos(u−v)=cosucosv+sinusinv

Here u is interchanged by v . Therefore

  cos(v−u)=cosvcosu+sinvsinu

Substitute:

  sinu=−725,cosu=−2425,sinv=−35

And,

  cosv=−45

So,

  cos(u+v)=(−45)(−2425)+(−35)(−725)=96125+21125=117125

Therefore,

  cos(v−u)=117125 .

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Chapter 5.4, Problem 49E
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Chapter 5.4, Problem 51E

Chapter 5 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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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