Vectorial Analysis , convert from Cartesian (x,y,z) to Cylindrical (ρ,θ,z) r= $5t^2 $ 
$\sqrt{1-t^2}$ i +$5t^3$j + $3t^2$ k
I was trying to convert that exercice and find 
speed and acceleration in cilindrycal coordinates but somehow I got lost because what I have
$x=pcos\theta$;
$y=psen\theta$;
z=z
and $e\theta$ =-$sen\theta$i+$cos\theta$j,
$ep$ =$cos\theta$i+$sen\theta$j
ez=ez
When I try to convert I always got messy results with $cos\theta$ and $sen\theta$
REsult:
r= $10tep$i + $5t^2 $ /
$\sqrt{1-t^2}$$e$$\phi$j + 6$tk$
I would appreciate your help.

We have that


*

*$x=5t^2\sqrt{1-t^2}$

*$y=5t^3$

*$z=3t^2$


then


*

*$\rho=\sqrt{x^2+y^2}=\sqrt{25t^4(1-t^2)+25t^6}=5t^2$


since $x$ is always positive


*

*$\theta = \arctan \frac{y}{x}=\arctan \frac{t}{\sqrt{1-t^2}}$

