## q-Sine

The q-Analog of the Sine function, as advocated by R. W. Gosper, is defined by

where is a Theta Function and is defined via

This is a period , Odd Function of unit amplitude with double and triple angle formulas and addition formulas which are analogous to ordinary Sine and Cosine. For example,

where is the q-Cosine, and is q-Pi.

Gosper, R. W. Experiments and Discoveries in -Trigonometry.'' Unpublished manuscript.