I know very little about this subject but I've heard Euler's name and Quaternions suggested for solutions. If I have a base system using X and Y, and I know I can convert Cosine values (as X) into Sine Values (yielding negative Y) by deriving Cosine, or convert from Sine (as Y) to Cosine (as X) by deriving Sine, how can I get to the Z axis?
More Generally, is Trigonometry limited only to 2 dimensional circles? Are there no variants of Sine/Cos/Tan and Derivatives that work with coordinates in the VOLUME of Spheres or n-spheres and so on?
My gut tells me the imaginary plane of i could double as a Z axis but somehow this seems like it is not the answer. Bottom line, why can we convert from X to Y, but not X-> Z or Y->Z without creating a mess with the relationship of X and Y?