Example 3

Spherical Coordinates are defined by
x=rcos(theta)sin(phi)
y=rsin(theta)sin(phi)
z=rcos(phi)
r>=0, 0<=theta<=2Pi, 0<=phi<=Pi

In[37]:=

  Clear[r,theta,phi,x,y,z]

In[38]:=

  x[r_,t_,p_]:=r Cos[t] Sin[p]
  y[r_,t_,p_]:=r Sin[t] Sin[p]
  z[r_,t_,p_]:=r Cos[p]

In[39]:=

  x[r,theta,phi]
  y[r,theta,phi]
  z[r,theta,phi]

Out[39]=

  r Cos[theta] Sin[phi]

Out[40]=

  r Sin[phi] Sin[theta]

Out[41]=

  r Cos[phi]

In[42]:=

  Clear[a,b,c]
  {a,b,c}=Simplify[scalefactors[x,y,z][r,theta,phi]]

Out[42]=

            2         2         2
  {1, Sqrt[r  Sin[phi] ], Sqrt[r ]}