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Solve for θ: 3 tan³ θ = tan θ

by Patrick
(Ohio, USA)











































Solve for θ

   • Solve the given equation for θ.

          3 tan³ θ = tan θ

   • The solution

          Enter your answers as a comma-separated list.

          Let k be any integer.

          Round terms to three decimal places where appropriate.

          If there is no solution, enter NO SOLUTION.

Comments for Solve for θ: 3 tan³ θ = tan θ

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Oct 24, 2012
Solve for θ
by: Staff

Answer


         Solve for θ


3 tan³ θ = tan θ

Divide each side of the equation by tan θ

3 * tan³ θ tan θ
-------------- = ---------
tan θ tan θ

3 * tan³ θ tan θ
-------------- = -------------
tan θ tan θ

3 * tan³ θ
-------------- = 1
tan θ

3 * tan θ * tan² θ
----------------------- = 1
tan θ

3 * tan θ * tan² θ
----------------------- = 1
tan θ

3 tan² θ = 1

Divide each side of the equation by 3

3 * tan² θ 1
-------------- = -----
3 3

3 * tan² θ 1
-------------- = ------
3 3

1
(1) * tan² θ = -----
3

1
tan² θ = -----
3

Take the square root of each side of the equation

1
√(tan² θ) = √(-----)
3

1
tan θ = ± √(-----)
3

√1
tan θ = ± ------
√3

1
tan θ = ± ------
√3

To rationalize the denominator, multiply
the right side of the equation by √3/√3

1 √3
tan θ = ± ----- * ------
√3 √3

1 * √3
tan θ = ± -------------
√3 * √3

√3
tan θ = ± -------
3

θ = tan⁻¹[±√(3) / 3]

θ = tan⁻¹[±1.7320508075689 / 3]

θ = tan⁻¹[±0.5773502691896]

θ = 30°, 150°, 210°, 330°

(or θ = 1pi/6 radians, 5pi/6 radians,
7pi/6 radians, 11pi/6 radians)

θ =180k + 30

θ =180k - 30

Final Answer:

θ (in degrees) = 180k ± 30



Thanks for writing.

Staff
www.solving-math-problems.com


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