Suppose you have an elliptical orbit like this one here. What I have are 2D polar coordinates for any point on it, and the inclination of the ellipse's plane with regard to the reference plane. What I want to do is to obtain the Cartesian coordinates of any such point.
So, what I have given is:
d - distance from the primary, a - azimuth on the ellipse's plane (true anomaly), i - inclination of the ellipse's plane to the reference plane.
From this, I want to get the x, y, z coordinates. According to various sources, the formulas are:
x = d*sin(theta)*cos(phi)
y = d*sin(theta)*sin(phi)
z = d*cos(theta)
Of these, I seem only to have the d. How do I divine theta and phi from the available data?