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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Fundamentals of Trigonometric Identities
Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.
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Question
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Chapter 5, Problem 78RE
To determine

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

Expert Solution & Answer
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Answer to Problem 78RE

  sin(u−v)=−44125 .

Explanation of Solution

Given information:

Given expression,

  sin(u−v)

  u is in quadrant I and v is in quadrant III.

Calculation:

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

The sine of an angle is equal to opposite side over the hypotenuse. Since sinu=45 and u is quadrant I. So, the following figure will obtain:

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

Therefore:

  cosu=35

The cosine of an angle is equal to adjacent side over the hypotenuse. Since cosv=−725 and v is in quadrant III.. So, the following figure will obtain:

  Precalculus with Limits: A Graphing Approach, Chapter 5, Problem 78RE

Since the sineof an angle is equal to opposite side over the hypotenuse and v is in quadrant III.. Therefore:

  sinv=−2425

Apply the difference formula for sine that is:

  sin(u−v)=sinucosv−cosusinv

Substitute:

  sinu=45,cosu=35,sinv=−2425

And,

  cosv=−725

So,

  sin(u−v)=(45)(−725)−(35)(−2425)=−28125+72125=−44125

Therefore,

  sin(u−v)=−44125 .

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Chapter 5, Problem 77RE
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Chapter 5, Problem 79RE

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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Fundamental Trigonometric Identities: Reciprocal, Quotient, and Pythagorean Identities; Author: Mathispower4u;https://www.youtube.com/watch?v=OmJ5fxyXrfg;License: Standard YouTube License, CC-BY