Cylindrical / Spherical Coordinates

[eurekameh]

I'm trying to convert the below Cartesian coordinate system into cylindrical and spherical coordinate systems. For the cylindrical system, I had r,vector = er,hat + sint(e3,hat).
While I do have a technically correct answer for the spherical coordinate system, I believe, I was wondering if there was a way to simplify the expression 1/cos[tan^-1*(sint)]. Thanks.

 

[mfb]

$r=\sqrt{x^2+y^2+z^2} = \sqrt{1+\sin^2(t)}$?

 

[eurekameh]

rad(1+sin^2(t)) = 1/(cos(tan^-1(sint)))?
Also, am I right in thinking r = rad(x^2 + y^2) = 1 for cylindrical coordinates?

 

[mfb]

rad(1+sin^2(t)) = 1/(cos(tan^-1(sint)))?

Would be interesting to check this in an analytic way.

Also, am I right in thinking r = rad(x^2 + y^2) = 1 for cylindrical coordinates?

If you use (r,theta,z) as coordinates: Right.