Chapter 7: Triple Integration
Section 7.5: Spherical Coordinates
Example 7.5.2
Express the spherical point ρ,φ,θ=2,π/3,π/6 in Cartesian coordinates.
Solution
Mathematical Solution
Substitution into the equations on the left in Table 7.5.1 leads to
x=2 cosπ6sinπ3 = 32
y=2 sinπ6sinπ3 = 32
z=2 cosπ3 = 1
Maple Solution - Interactive
Expression palette: Evaluation template Press the Enter key.
ρ cosθsinφ,ρ sinθsinφ,ρ cosφx=a|f(x)ρ=2,φ=π3,θ=π6
32,123,1
Maple Solution - Coded
Use the eval command to make substitutions into the equations on the left in Table 7.5.1.
evalρ cosθsinφ,ρ sinθsinφ,ρ cosφ,ρ=2,φ=π/3,θ=π/6
The only tool in Maple for converting coordinates of a point is the MapToBasis command in the Student VectorCalculus package, a package in which points are represented as vectors. The Vector command must be used to cast the given point into spherical coordinates. The BasisFormat command sets the display mode for vectors in this package.
Initialize
Install the Student VectorCalculus package.
Set the display format for vectors.
withStudent:-VectorCalculus:BasisFormatfalse:
Change to spherical coordinates
MapToBasisVector2,π/3,π/6,spherical,cartesian =
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