anonymous 4 years ago Solve the equation! 3 tan^3θ = tan θ

1. tkhunny

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

2. anonymous

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).

3. tkhunny

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

4. anonymous

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

5. tkhunny

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

6. anonymous

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?

7. lopus

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