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for arguments sake, let's say I'm trying to find spherical coordinates from say (45,90) (latitude,longitude) on the earth, and then convert that result back into cartesian coordinates. I realize this seems counterintuitive since I already have the exact coordinates, but I do not have the coordinates relative to the location. What I want to be able to do is find the location on the planet setting (45,90) as the zero of the spherical axis so that I can then convert it back to cartesian coordinates and get the exact location. Is there some kind of transformation I'm overlooking which makes this possible?

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    The earth is better modeled by an ellipsoid. Depending on the accuracy you need this is an important consideration. – 2017-01-17

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Up to factors of $\frac {\pi}{180}$ and the direction of measurement, latitude and longitude are spherical coordinates. If we assume a spherical earth, you have the coordinates. The radius is $R_e$ the radius of the earth. $\theta$, the polar angle is $90^\circ$ minus the latitude. $\phi$, the azimuthal angle is the longitude. You can convert it to Cartesian by the usual approach: $x=R_e \sin \theta \cos \phi$ and so on.

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    I must have not explained myself very clearly. As I did state, I realize how to get any coordinates from the spherical system, what I want to know how to do is translate the zero of the spherical coordinate system relative to the cartesian system. Because if for example I had two points on the sphere and I used each of them as zeros for the spherical coordinate system, the arc of each one would not align with the arc of the other, and that is my problem. – 2017-01-17
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    The zero of both the Cartesian and spherical systems is at the center of the earth. The point at latitude 0, longitude 0 on the surface of the earth has coordinates $(R_e,0,0)$ in the Cartesian system and $(R_e,90^\circ,0)$ in the spherical if you use the usual spherical angles measuring $\theta$ down from the $z$ axis. – 2017-01-17