# q-Trigonometric Functions

q-Trigonometric Functions

The -analogs of trigonometric functions are built out of -exponentials in the same way that the classical trigonometric functions are built out of the classical exponential function. The existence of two flavors of -exponents makes for two kinds of -trigonometric functions: and for and and for . These triples are plotted for various on the interval . You can see how the -analogs approach their classical counterparts as tends to 1.

q

q

q

q

sin(x)

q

Sin(x)

q

sin(x)

cos(x)

q

Cos(x)

q

cos(x)

0<q<1

0<u<2π

q

q