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


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


  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]


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


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