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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.


	Contributed by: Oleksandr Pavlyk
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The

-sine and

-cosine functions can also be defined by the following series:

;

The

-sine and

-cosine functions have

-analogs of the defining algebraic identity satisfied by their classical counterparts:

. Additionally they satisfy

V. Kac and P. Cheung, Quantum Calculus, New York: Springer, 2001.

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