ABSTRACT
The properties of the hyperbolic trigonometric functions look very much
like their ordinary trigonometric counterparts (except for signs). This sim-
ilarity derives from the identities
coshβ ≡ cos(iβ), (4.10) sinhβ ≡ −i sin(iβ). (4.11)
4.2 DISTANCE We saw in Chapter 3 that Euclidean trigonometry is based on circles, sets
of points that are a constant distance from the origin. Hyperbola geometry
is obtained simply by using a different distance function. Measure the
“squared distance” of the point B with coordinates (x, y) from the origin
by using the definition
ρ2 = x2 − y2. (4.12) This distance function is the key idea in hyperbola geometry.
