Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

So if I have an equation for a torus in $F(a,b) = (X, Y, Z)$ where $X = (R + r\cos a)\cos b$ and $0 < r < R$, how would I go about rewriting this equation for $X$ in terms of $\tan(a/2)$ and $\tan(b/2)$? I'm having a hard time doing the conversion. This might seem like an odd question but it's just the first step to a larger problem I'm working on but once I got this I'm good to go.

share|cite|improve this question
    
Are $x$, $y$ and $z$ functions of $a$ and $b$? Is $X$ the same as $x$? – Fly by Night Feb 23 '13 at 18:46
    
Sorry I should have been more clear in my notation. x and X are the same. My question boils down to simply rewriting the equation X = (R+rcosa)cosb in terms of tan(a/2) and tan(b/2) instead of cosa and cosb or just in some form that incorporates those tangents – user1855952 Feb 23 '13 at 18:48

Hint: $$\sin a = 2\sin(a/2)\cos(a/2) = 2\tan(a/2)\cos^2(a/2) = \frac{2\tan(a/2)}{1+\tan^2(a/2)} $$ $$\cos a =\cdots$$

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.