Converting cartesian parametric coordinates to cylindrical or spherical coordinates

Question

How could I change these parametric equations in cartesian coordinates to cylindrical or spherical coordinates?

$x(t) = \cos(t)$

$y(t) = \sin(t)$

$z(t) = \sin(t)$

If someone could give me some tips it would be awesome. Thanks in advance.

Answer 1

In Cylindrical coordinates we have $$ \rho \cos \theta=\cos t $$$$ \rho \sin \theta=\sin t $$ $$ z=\sin t $$ and, for $-\pi/2< \theta< \pi/2$ this gives $$ \theta =t ,\quad, \quad \rho=1 \quad ,\quad z=\sin t $$ I think that you can solve in the same manner for the spherical coordinates