Given an arc length and an angle, how do I get a sphere coordinate?

Question

Assuming I start at the top of a sphere and am given the radius of the sphere, an angle to turn, and a distance to walk along the sphere, how could I find my destination in the sphere coordinate system (r, θ, φ), where r is the radius, θ is the polar angle, and φ is the azimuthal angle?

Answer 1

You know $r$. $\phi$ is the angle you are told to turn. If you are told to walk a distance $d$, $\theta$ is simply $d/r$. (I am working in angle units of radians here.)