Question

Solve the equation!

3 tan^3θ = tan θ

Answer 1

Just like you used to solve polynomials back in algebra. Collecte everything to one side. Factor everything. Give it a go!

Answer 2

lol dont need to go that far.
let x = tan(theta),
then 3x^3 = x, so either x = 0, or you can divide x from both sides to get: 3x^2 = 1
so x can be 0, 1/sqrt(3), or -1/sqrt(3).

Answer 3

In other words, collect and factor. Of course, you should solve the actual problem by finding the angle that gives these tangents.

Answer 4

now I need to find all real solutions with k being any integer.

Answer 5

You have \(\tan(\theta) = 0\), \(\tan(\theta) = \dfrac{1}{\sqrt{3}}\), and \(\tan(\theta) = \dfrac{-1}{\sqrt{3}}\). Track them down.

Answer 6

ok, so...for tan(θ)=0 I get 0 and pi. for tan(θ)=1/√3 I get pi/6 and 7pi/6. And for tan(θ)=−1/√3 I get 5pi/6 and 11pi/6. how do I know if I would add pi k to each or 2pi k?