|Dec8-08, 11:07 AM||#18|
Also, the Pythagorean Theorem has to hold as well: x2 + y2 + z2 = r2.
x2 + y2 + z2
= (r sin θ cos ϕ)2 + (r sin θ sin ϕ)2 + (r cos θ)2
= r2 sin2 θ cos2 ϕ + r2 sin2 θ sin2 ϕ + r2 cos2 θ
= r2 (sin2 θ (cos2 ϕ + sin2 ϕ) + cos2 θ)
= r2 (sin2 θ + cos2 θ)
Also, as a general note, observe that x and y depend on both angles, so they both better be in the equations for them.
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