EBK PRECALCULUS W/LIMITS
EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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Question
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Chapter 5, Problem 64RE
To determine

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

Expert Solution & Answer
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Answer to Problem 64RE

  sin2u=−45cos(2u)=35tan(2u)=−43 .

Explanation of Solution

Given information:

Given trigonometric ratio

  cosu=−25,     π2<u<π .

Calculation:

Consider the ratio

  cosu=−25,     π2<u<π

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 π2<u<π , draw the triangle;

  EBK PRECALCULUS W/LIMITS, Chapter 5, Problem 64RE

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 63RE
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Chapter 5, Problem 65RE

Chapter 5 Solutions

EBK PRECALCULUS W/LIMITS

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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