Why converting from Spherical to Cartesian using the command "sph2cart" gives different values than converting it manually by writing the equations of each coordinate?

[Reem]

Even when Cylindrical to Cartesian and the rest

Answer 1

[Voss]

Assuming theta is azimuth and phi is elevation, your equations would be (from the documentation):

x = r .* cos(phi) .* cos(theta)

y = r .* cos(phi) .* sin(theta)

z = r .* sin(phi)

Making those corrections gives:

r = 10;
theta = pi/4;
phi = pi/3;

x = r*cos(phi)*cos(theta)

x = 3.5355

y = r*cos(phi)*sin(theta)

y = 3.5355

z = r*sin(phi)

z = 8.6603

And note that the order of the inputs to sph2cart is azimuth before elevation:

[x,y,z] = sph2cart(theta,phi,r)

x = 3.5355

y = 3.5355

z = 8.6603