In order to use ParametricPlot3D to graph things in spherical and cylindrical coordinates, you must first develop a "change of variable" function. Show that they are really the same surface. These two graphs look suspiciously alike. (If you had used the Plot3D function instead, it would have looked a little nicer.) You can even use ParametricPlot3D to graph a function of 2 variables: If you like, you can use ParametricPlot3D to draw a surface: If it annoys you, you can get rid of it by the following: It will then graph the range of the function. ParametricPlot3D requires a function from either or as an input. Both of these commands are based on a much more flexible command, ParametricPlot3D. For example, they wouldn't be capable of plotting something as simple as. Unfortunately, these aren't really as versatile as we might wish. Mathematica has special built-in functions for graphing cylindrical and polar coordinates (CylinderPlot3D and SphericalPlot3D). ParametricPlot3D with spherical and cylindrical coordinates
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