# Math Help - Parametric equations

1. ## Parametric equations

I have just been doing an integration question where I was asked to use substitution $y=2Asin^2(u/2)$. so now i have done the integration

and got $x-B=4A^{2}(u-sin(u))$ and I need to show the parametric solution is

y=A(1-cos(u)) and x=A(u-sin(u))+B

Ok so if $y=2Asin^2(u/2)$, then y=A(1-cos(u)) but how to get x?

2. ## Re: Parametric equations

I do not know if that work for you

$y = A ( 1- \cos u ) \Rightarrow u = \cos ^{-1} \left( 1 - \frac{y}{A}\right)$

$x = A ( u - \sin u ) + B$

$x = A \left[ \cos ^{-1} \left( 1 - \frac{y}{A}\right) - \sin \left(\cos ^{-1} \left( 1 - \frac{y}{A}\right) \right)\right] + B$

it is better to post the whole question

3. ## Re: Parametric equations

Can you tell us how you got $x$ in the first place?