The curve C has parametric equations

$\displaystyle x=cos^3\theta$

$\displaystyle y=sin^3\theta$

$\displaystyle 0<=\theta.=\frac{\pi}{2}$

a) find the arc length of C.

b) The curve C is rotated through 4 right angles about the x-axis. find the area of the curve surface generated.

OK so I've learned everything now for FP3 it's just a case of putting it into practice. Also my notes are slightly hard to understand in some places lol.

part A i would think differentiate x, then differentiate y, then form dy/dx

getting

$\displaystyle \frac{dy}{dx}=\frac{3cos^2\theta}{-3sin^2\theta}$

thats what i did initally but looking at my notes it looks more like differentiation from first principles ... and pythagoras ... so i'm a bit stumped