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 44E
To determine

To find:The solution of the equation tan4θ13tan2θ+36=0 .

Expert Solution & Answer
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Answer to Problem 44E

The solutions of the equation tan4θ13tan2θ+36=0 are θ=1.11+kπ , θ=1.11+kπ , θ=1.25+kπ and θ=1.25+kπ .

Explanation of Solution

Given information:

The given equation is tan4θ13tan2θ+36=0 .

Calculation:

Simplify the given equation.

  tan4θ13tan2θ+36=0tan4θ9tan2θ4tan2θ+36=0(tan2θ4)(tan2θ9)=0

First substitute the factor tan2θ4=0 .

Simplify the equation

  tan2θ4=0tan2θ=4tanθ=±2

As tangent has period π . So first find the solutions in (π2,π2) .

Therefore, the solution to the equation in (π2,π2) are

  θ=tan1(2)1.11

And,

  θ=tan1(2)1.11

As tangent repeats its values after every π units.

So, the general solution of the equation is given by

  θ=1.11+kπ,1.11+kπ

Therefore, the solutions of the equation tan2θ4=0 are θ=1.11+kπ and θ=1.11+kπ .

Now substitute the factor tan2θ9=0 .

Simplify the equation

  tan2θ9=0tan2θ=9tanθ=±3

As tangent has period π . So first find the solutions in (π2,π2) .

Therefore, the solution to the equation in (π2,π2) are

  θ=tan1(3)1.25

And,

  θ=tan1(3)1.25

As tangent repeats its values after every π units.

So, the general solution of the equation is given by

  θ=1.25+kπ,1.25+kπ

Therefore, the solutions of the equation tan2θ9=0 are θ=1.25+kπ and θ=1.25+kπ .

Combining all the solutions give the solution of the equation tan4θ13tan2θ+36=0 .

Therefore, the solutions of the equation tan4θ13tan2θ+36=0 are θ=1.11+kπ , θ=1.11+kπ , θ=1.25+kπ and θ=1.25+kπ .

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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