Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Dama28

  • 3 years ago

Solve the equation! 3 tan^3θ = tan θ

  • This Question is Closed
  1. tkhunny
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  2. cnknd
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  4. Dama28
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  5. tkhunny
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  6. Dama28
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1353819049038:dw|

  8. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy