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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Concept explainers

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 75CR
To determine

To calculate: The exact value of the trigonometric expression.

Expert Solution & Answer
Check Mark

Answer to Problem 75CR

The required exact value is 44125 .

Explanation of Solution

Given information:

The trigonometric expression: sin(u+v)

  sinu=45

  cosv=−725

Formula used:

Trigonometric formula:

  sin(u+v)=sinucosv+cosusinv

Pythagoras Theorem:

For a right-angle triangle;

  Hypotenuse2=Perpendicular2+Base2h2=p2+b2

Calculation:

The given trigonometric expression is sin(u+v) .

Also, sinu=45

  cosv=−725

To find the exact value of the given expression, use the formula sin(u+v)=sinucosv+cosusinv .

Here, for sinu=45 ;

Perpendicular, p = 4 and Hypotenuse, h = 5

By Pythagoras Theorem;

  Hypotenuse2=Perpendicular2+Base2h2=p2+b2

So, h2=p2+b2b=h2−p2b=52−42b=3

And, cosu=bh=35

Also, for cosv=−725 ;

Base, b = 4 and Hypotenuse, h = 5

By Pythagoras Theorem;

  Hypotenuse2=Perpendicular2+Base2h2=p2+b2

So, h2=p2+b2p=h2−b2p=252−(−7)2b=24

And, sinv=ph=2425

Now, substitute 45 for sinu , 35 for cosu , 2425 for sinv and −725 for cosv in the formula sin(u+v)=sinucosv+cosusinv .

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

Hence, the required exact value is 44125 .

Previous
Chapter 5, Problem 74CR
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Chapter 5, Problem 76CR

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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Prob. 34ECh. 5.4 - Prob. 35ECh. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Prob. 40ECh. 5.4 - Prob. 41ECh. 5.4 - Prob. 42ECh. 5.4 - Prob. 43ECh. 5.4 - Prob. 44ECh. 5.4 - Prob. 45ECh. 5.4 - Prob. 46ECh. 5.4 - Prob. 47ECh. 5.4 - Prob. 48ECh. 5.4 - Prob. 49ECh. 5.4 - Prob. 50ECh. 5.4 - Prob. 51ECh. 5.4 - Prob. 52ECh. 5.4 - Prob. 53ECh. 5.4 - Prob. 54ECh. 5.4 - Prob. 55ECh. 5.4 - Prob. 56ECh. 5.4 - Prob. 57ECh. 5.4 - Prob. 58ECh. 5.4 - Prob. 59ECh. 5.4 - Prob. 60ECh. 5.4 - Prob. 61ECh. 5.4 - Prob. 62ECh. 5.4 - Prob. 63ECh. 5.4 - Prob. 64ECh. 5.4 - Prob. 65ECh. 5.4 - Prob. 66ECh. 5.4 - Prob. 67ECh. 5.4 - Prob. 68ECh. 5.4 - Prob. 69ECh. 5.4 - Prob. 70ECh. 5.4 - Prob. 71ECh. 5.4 - Prob. 72ECh. 5.4 - Prob. 73ECh. 5.4 - Prob. 74ECh. 5.4 - Prob. 75ECh. 5.4 - Prob. 76ECh. 5.4 - Prob. 77ECh. 5.4 - Prob. 78ECh. 5.4 - Prob. 79ECh. 5.4 - Prob. 80ECh. 5.4 - Prob. 81ECh. 5.4 - Prob. 82ECh. 5.4 - Prob. 83ECh. 5.4 - Prob. 84ECh. 5.4 - Prob. 85ECh. 5.4 - Prob. 86ECh. 5.4 - 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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