1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Solving for Theta, wolfram doesn't give anything useful

  1. Sep 17, 2012 #1
    1. The problem statement, all variables and given/known data
    I need to write a function of theta in terms of a particular variable. I just can't seem to figure it out; the only solution I can come up with is when the aforementioned variable is equal to 0 or 1. I'm using Q to denote theta, and b is the variable.


    2. Relevant equations
    Any and all trig identities.
    I've used sin^2(x)+cos^(x)=1, sin(2x)=2sin(x)cos(x), I haven't stumbled into any work that led me to use other identities!

    3. The attempt at a solution
    Around 5 pages of scratch work, all for naught.
    Any relevant trig identities I might be missing would be nice to know, if anyone figures this out soon! Thanks!
  2. jcsd
  3. Sep 17, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    sin3(θ)/cos(θ) = 1/(cot(θ)csc2(θ)) = 1/(cot(θ)+cot3(θ))

    but I don't think this will help all that much.
  4. Sep 17, 2012 #3


    User Avatar
    Science Advisor
    Homework Helper

    You can reduce it to a polynomial equation. Square both sides. Replace cos(Q)^2 by 1-sin(Q)^2. Now let P=sin(Q)^2. You'll get a cubic equation in P. You CAN solve a cubic exactly, but the solutions are so complicated as to be almost useless. You will have a little advantage here because there is no P^2 term. But it's still pretty complicated. Stuff like this is usually handled numerically, not analytically.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook