2d circle in a 3d world...

hi
im trying to make a stickman type animation in 3d (the stickman is still made up of lines but you can rotate around him and so on)
trying to draw the circle for the face and so far i have a loop which calculates so many points around the circle:

the centre of the circle is given by cx,cy,cz, the radius by r, the horizontal angle from the x-axis is theta and the vertical angle from the vertical axis is phi.

i can easily calculate the positions of points on the circle in 2d, but translating it into 3d with the theta and phi angles is proving.... tricky

Couldn't you just calculate the points on the circle given that the axis on the plane, say the z axis, for points only on the z-y plane?