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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Chapter 5, Problem 92RE
To determine

To find: the exact value of sin2u,cos2u and tan2u , using the double angle formulas.

Expert Solution & Answer
Check Mark

Answer to Problem 92RE

  sin2u=45cos(2u)=35tan(2u)=43 .

Explanation of Solution

Given information:

Given trigonometric ratio

  cosu=−25,     π<u<3π2 .

Calculation:

Consider the equation

  cosu=−25,     π<u<3π2

Find sin2u using double angle formula. The cosineof an angle is equal to adjacent side over the hypotenuse. Since;

  cosu=−25

Apply Pythagorean Theorem to find length of opposite side;

  5−22=±1=±1

Take only −1 because π<u<3π2 , draw the triangle;

  Precalculus with Limits: A Graphing Approach, Chapter 5, Problem 92RE

Therefore;

  sinu=OppositeHypotenuse=−15

And,

  tanu=Oppositeadjacent=12

Apply double angle formula sin2u=2sinucosu . Substitute sinu=−15 and cosu=−25 ;

  sin2u=2(−15)(−25)=45

Therefore sin2u=45

Apply double angle formula cos2u=cos2u−sin2u . Substitute sinu=−15 and cosu=−25 ;

  cos2u=(−25)2−(−15)2=45−15=35

Therefore cos(2u)=35

Find tan(2u) using double angle formula; apply double angle formula for tangent

  tan2u=2tanu1−tan2u

Substitute; tanu=12

  tan2u=2(12)1−(12)2=(134)=43

Therefore;

  tan(2u)=43 .

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Chapter 5, Problem 91RE
Next
Chapter 5, Problem 93RE

Chapter 5 Solutions

Precalculus with Limits: A Graphing Approach

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Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning
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