  There exists a well-known relation between the zeros of sine function,
Bernoulli numbers and the Riemann Zeta function. In the present paper, we find
a similar relation for zeros of q-sine function. We introduce a new q-extension
of the Bernoulli numbers with generating function written in terms of both
Jackson's q-exponential functions. By q-generalized multiple product Leibnitz
rule and the q-analogue of logarithmic derivative we established exact
relations between zeros of q-sin x and our q-Bernoulli numbers. These relations
could be useful for analyzing approximate and asymptotic formulas for the zeros
and solving BVP for q-Sturm-Liouville problems.
