# Thread: Spherical Vector To Cartesian Vector

1. ## Spherical Vector To Cartesian Vector

Hello everyone,

I have a quick and straightforward problem, that I need some help with.

Suppose I have a spherical vector defined by a radius and two angles, denoted by <rho,theta,psi>. Where, rho is the radius, theta is an angle, and so is psi.

Which that being said, how would I convert that spherical vector into a Cartesian vector.

(Note: I know how to convert from Spherical to Cartesian;
x=rho*sin(psi) *cos(theta)
Y=rho*sin(psi) *sin(theta)
Z=rho*cos(theta)

Would these conversion also be appropriate if the input is a spherical vector, and the required output is a Cartesian vector.

Thanks for the help.
Taylor S. Amarel
Learning is living

2. theta is an angle, and so is psi.

with respect to what? Which one is the reference line?

3. Theta= The angle of rotation around Y on the XZ plane
Psi= The angle of rotation around Z on the YX plane

So the reference direction would be X? Is that right, if I knew the formula I am sure I could swap variables out into their proper location for my coordinate system

4. Your equations to convert from spherical to cartesian are incorrect. The x and y must have sin(theta) in them, where theta is the polar angle (measured down from the positive z axis), and z must have cos(theta) in it. What changes in x and y is the trig function of the azimuthal angle (measured around the z axis).

5. So if I understand you correctly, the conversion would be as follows.
x=rho*sin(theta)*cos(psi)
y=rho*sin(theta)*sin(psi)
z=rho*cos(theta)
I am correct?

6. That is correct. Does this solve your problem?

7. ## Thank You!

Originally Posted by Ackbeet
That is correct. Does this solve your problem?
Yes, indeed it does. Kudos for the help, and have a good day.

Thanks,
Taylor S. Amarel
Learning is Living

8. You're welcome. Have a good one!