# Spacetime Trig Functions Graph

QMN:1010.0822

abstract:

This one-page figure shows the relationships between sin/cos/tan and their hyperbolic counterparts for events in spacetime. The standard trig functions are the three pairwise ratios: sine -> far/hypothenuse, cosine -> near/hypothenuse, tangent -> far/near. What is not often known is the hyperbolics are even simpler, being only about one side of a trinage made to the hyperbola: sine -> far, cosine -> near, tanget -> hypothenuse. Any point in spacetime can be plotted using Euclidean, polar (scaled signs and cosines) or hyberbolic coordinates (scaled hyperbolic sines and cosines).