Note: This only works when \(x\) is measured in radians. We are now going to look at more complex trigonometric functions where we will use the general rule: \(\int {\cos (ax + b)dx = \frac{1}{a}} ...

Trigonometric sums and summation formulas have long served as essential tools for elucidating periodic phenomena across mathematics and the physical sciences. These techniques entail the explicit ...

Using the q-trigonometric definitions of Gosper, we devise a new q-exponential function. Based on this concept, we derive a number of identities involving the Jacobi theta functions. These ...