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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Chapter 7.4, Problem 56E
To determine

To find: The solution of the equation 4cosθsinθ+3cosθ=0 .

Expert Solution & Answer
Check Mark

Answer to Problem 56E

The solutions of the equation 4cosθsinθ+3cosθ=0 are θ=π2+kπ and θ=3.99+2kπ and θ=5.44+2kπ .

Explanation of Solution

Given information:

The given equation is 4cosθsinθ+3cosθ=0 .

Calculation:

Simplify the equation.

  4cosθsinθ+3cosθ=0cosθ(4sinθ+3)=0

First substitute the factor cosθ=0 .

As cosine has period 2π . So first find the solutions in [0,2π) .

Therefore, the solution to the equation in [0,2π) are

  θ=cos1(0)=π2,3π2

As cosine repeats its values after every 2π units.

So, the general solution of the equation is given by

  θ=π2+2kπ,3π2+2kπ=π2+kπ

Therefore, the solutions of the equation cosθ=0 are θ=π2+kπ .

Now substitute the factor 4sinθ+3=0 .

Simplify the equation.

  4sinθ+3=04sinθ=3sinθ=34

As sine has period 2π . So first find the solutions in [0,2π) .

Therefore, the solution to the equation in [0,2π) are

  θ=sin1(34)3.99,5.44

As sine repeats its values after every 2π units.

So, the general solution of the equation is given by

  θ=3.99+2kπ,5.44+2kπ

Therefore, the solutions of the equation 4sinθ+3=0 are θ=3.99+2kπ and θ=5.44+2kπ .

Therefore, the solutions of the equation 4cosθsinθ+3cosθ=0 are θ=π2+kπ and θ=3.99+2kπ and θ=5.44+2kπ .

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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(a) sin 8...Ch. 7 - For the angles and in the figures, find cos( +...Ch. 7 - Prob. 5TCh. 7 - Prob. 6TCh. 7 - Prob. 7TCh. 7 - Prob. 8TCh. 7 - Find the exact value of cos(2tan1940).Ch. 7 - Rewrite the expression as an algebraic function of...Ch. 7 - Wave on a Canal A wave on the surface of a long...Ch. 7 - Prob. 2PCh. 7 - Traveling Wave A traveling wave is graphed at the...Ch. 7 - Traveling Wave A traveling wave has period 2/3,...Ch. 7 - Standing Wave A standing wave with amplitude 0.6...Ch. 7 - Prob. 6PCh. 7 - Prob. 7PCh. 7 - Prob. 8PCh. 7 - Prob. 1CRTCh. 7 - Prob. 2CRTCh. 7 - Prob. 3CRTCh. 7 - Prob. 4CRTCh. 7 - Prob. 5CRTCh. 7 - Prob. 6CRTCh. 7 - Prob. 7CRTCh. 7 - Prob. 8CRTCh. 7 - Prob. 9CRTCh. 7 - Prob. 10CRTCh. 7 - Prob. 11CRTCh. 7 - Prob. 12CRT
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