Prove the Distance formula in Spherical Coordinates System?
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The length of the other leg of the right triangle is the distance from P to the z-axis, which is r=ρsinϕ. The distance of the point Q from the origin is the same quantity. ... In summary, the formulas for Cartesian coordinates in terms of spherical coordinates are x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ.
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