Precalculus: Mathematics for Calculus - 6th Edition
Precalculus: Mathematics for Calculus - 6th Edition
6th Edition
ISBN: 9780840068071
Author: Stewart, James, Redlin, Lothar, Watson, Saleem
Publisher: Cengage Learning
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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 7.3, Problem 4E
To determine

To find: the valuesof sin2x,cos2x,tan2x .

Expert Solution & Answer
Check Mark

Answer to Problem 4E

  sin2x=−2425cos2x=−725tan2x=247 .

Explanation of Solution

Given information:

Given condition,

  tanx=−43

  x lies in Quadrant II

Formula used:

Double angle formula of sine

  sin2x=2sinxcosx=2tanx1+tan2x

Double angle formula of cosine

  cos2x=1−2sin2x=2cos2x−1=cos2x−sin2x=1−tan2x1+tan2x

Double angle formula of cosine

  tan2x=2tanx1−tan2x

Calculation:

Consider given conditions.

  tanx=−43

Calculate the value of sin2x by using the double angle formula as follows:

  sin2x=2tanx1+tan2x=2(−43)1+(−43)2=−831+169=−83259=−83(925)=−2425

Hence, sin2x=−2425 .

Calculate the value of cos2x by using the double angle formula as follows:

  cos2x=1−tan2x1+tan2x\=1−(−43)21+(−43)2=1−1691+169=−79259=−79(925)=−725

Hence, cos2x=−725 .

Calculate the value of tan2x by using the double angle formula as follows:

  tan2x=2tanx1−tan2x=2(−43)1−(−43)2=−831−169=−83−79=−83(−97)=247

Hence, tan2x=247 .

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Chapter 7.3, Problem 3E
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Chapter 7.3, Problem 5E

Chapter 7 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

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Prob. 60ECh. 7.5 - Prob. 61ECh. 7.5 - Prob. 62ECh. 7.5 - Prob. 63ECh. 7.5 - Damped Vibrations The displacement of a spring...Ch. 7.5 - Hours of Daylight In Philadelphia the number of...Ch. 7.5 - Belts and Pulleys A thin belt of length L...Ch. 7.5 - Prob. 67ECh. 7 - Prob. 1RCCCh. 7 - Prob. 2RCCCh. 7 - Prob. 3RCCCh. 7 - Prob. 4RCCCh. 7 - Prob. 5RCCCh. 7 - Prob. 6RCCCh. 7 - Prob. 7RCCCh. 7 - Prob. 8RCCCh. 7 - Prob. 1RECh. 7 - Prob. 2RECh. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - Prob. 11RECh. 7 - Prob. 12RECh. 7 - Prob. 13RECh. 7 - Prob. 14RECh. 7 - Prob. 15RECh. 7 - Prob. 16RECh. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - Prob. 19RECh. 7 - Prob. 20RECh. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - Prob. 27RECh. 7 - Prob. 28RECh. 7 - Prob. 29RECh. 7 - Prob. 30RECh. 7 - Prob. 31RECh. 7 - Prob. 32RECh. 7 - Prob. 33RECh. 7 - Prob. 34RECh. 7 - 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