Hi

I'm having some trouble working out how to convert from intrinsic to cartesian coordinates, and from cartesian to intrinsic, when the function is not given explicitly in terms of y. Let me show you a couple of problems which I have been unable to solve to illustrate this,

(1) The intrinsic equation of the curve is $\displaystyle s = \psi^2$. The curve passes through the point (2,0). Show that $\displaystyle x = 2(\cos\psi + \psi\sin\psi)$ and find y in terms of $\displaystyle \psi$

(2) For the curve with equation $\displaystyle \sin y = e^x$, wheresis measured from the point $\displaystyle (0,\frac{\pi}{2})$, show that $\displaystyle e^s = \tan \frac{\psi}{2}$

For the first I tried to let $\displaystyle \sqrt{s} = \psi$ and then take the cosine of both sides since $\displaystyle \frac{dx}{ds} = \cos\psi$ however I ended up with a bit of a mess and didn't really get anywhere.

For the second I tried to find an expression for $\displaystyle \frac{dy}{dx}$ and set it equal to $\displaystyle \tan\psi$ and also find the length of s, but I ended up with a horrible integral and again didn't really get anywhere.

I'm really at a loose end on how to solve these now, I think there must be something simple I'm missing, but I just can't see it.

Any help would be much appreciated, thanks

Stonehambey