Jacobi Elliptic Functions

sn(u,k), cn(u,k), dn(u,k) — the elliptic generalizations of sin, cos, and 1. As k→0 they reduce to trig functions; as k→1 they become hyperbolic. The modulus k controls the deformation. Live animation shows a pendulum whose exact solution is sn.

k = 0.60 | Period K(k) = —