Spherical Coordinates

The spherical coordinates $\left(\vphantom{ \rho ,\theta ,\phi }\right.$ρ, θ, φ$\left.\vphantom{ \rho ,\theta ,\phi }\right)$ locate a point P in space by giving the distance ρ from the origin, the angle θ projected onto the xy-plane (the polar angle), and the angle φ with the positive z-axis (the vertical angle). The conversion into rectangular coordinates is given by

x = ρsinφcosθ            y = ρsinφsinθ            z = ρcosφ

and the distance formula implies

ρ2 = x2 + y2 + z2

The default assumption is that ρ is a function of φ and θ. You can use other names for the polar and vertical angles. Any two variables you give will be interpreted as the polar and vertical angles. Even when you use the standard notation, however, the roles of the variables may be reversed in the default interpretation from what you intended. You can correct this interpretation with the Switch Variables option in the Plot Properties dialog box.

You can plot more than one surface on the same axes in the usual way.



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