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

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tkhunny
 3 years ago
Best ResponseYou've already chosen the best response.1Just like you used to solve polynomials back in algebra. Collecte everything to one side. Factor everything. Give it a go!

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0lol 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).

tkhunny
 3 years ago
Best ResponseYou've already chosen the best response.1In other words, collect and factor. Of course, you should solve the actual problem by finding the angle that gives these tangents.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0now I need to find all real solutions with k being any integer.

tkhunny
 3 years ago
Best ResponseYou've already chosen the best response.1You have \(\tan(\theta) = 0\), \(\tan(\theta) = \dfrac{1}{\sqrt{3}}\), and \(\tan(\theta) = \dfrac{1}{\sqrt{3}}\). Track them down.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ok, 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?
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