# 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

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

 Oct 24, 2012 Solve for θ by: Staff Answer         Solve for θ ` 3 tan³ θ = tan θDivide 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 = 1Divide 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 = ----- 3Take the square root of each side of the equation 1 √(tan² θ) = √(-----) 3 1 tan θ = ± √(-----) 3 √1 tan θ = ± ------ √3 1 tan θ = ± ------ √3To 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 - 30Final Answer: θ (in degrees) = 180k ± 30 ` Thanks for writing. Staff www.solving-math-problems.com