SphericalPlot3D Manipulate

Questions
1

a = ((3.14*.005) (1.887 - 1.792))/((.000522)*
Cos[-.7454Sin[[Theta]]Cos[[Phi]] + .6626Cos[[Theta]]]);
b = (1 - Cos[.7454Sin[[Theta]]Cos[[Phi]] + .6626
Cos[[Theta]]]^2)(1 -
Cos[-.7454Sin[[Theta]]Cos[[Phi]] + .6626Cos[[Theta]]])^2;
c = ab;
d = (Cos[c])^2;
SphericalPlot3D[d, {[Theta], 0, [Pi]}, { [Phi], 0, 2[Pi]}]

I have spherical 3D plot of some functions. Is there a way that I can manipulate this plot so that I vary theta from 0, pi/4 while I hold phi constant in the plot? Thank you in advance.

2

Perhaps the attached file will help.

3

Just to be clear, since there are more than one convention:
In SphericalPlot3D the first angle argument is the “latitudinal” angle. And the second angle argument is the “longitudinal” angle.
In the SphericalPlot3D case, the Mathematica documentation does not follow the most common uses of the greek letters theta and phi.

f[\[Theta]_, \[Phi]_] := Module[
  	{a, b, c, d},
  	a = ((3.14*.005) (1.887 - 1.792))/
        ((.000522)*Cos[-.7454*Sin[\[Theta]]*Cos[\[Phi]] + .6626*Cos[\[Theta]]]);
  	b = (1 - Cos[.7454*Sin[\[Theta]]*Cos[\[Phi]] + .6626*Cos[\[Theta]]]^2)* 
        (1 -Cos[-.7454*Sin[\[Theta]]*Cos[\[Phi]] + .6626*Cos[\[Theta]]])^2;
  	c = a*b;
  	d = (Cos[c])^2
  ]

  SphericalPlot3D[f[polar, azimuthal], {polar, 0, \[Pi]}, {azimuthal, 0, 5}]

Sphericalshell.png
Sphericalshell.png388×413 50.5 KB

4

SphericalPlot3D Manipulate