distorted sine function

Question

I'd like an easy way to numerically produce periodic functions that have the same min/max patterns as sine and cosine, but with fatter/skinnier widths of the humps. The extrema would still be at the same locations, just the parts between them would be stretched/compressed. What is a simple way to accomplish this, without resorting to many terms? It will be implemented in Numpy.

Answer 1

You can try $sin^k(x)$ and $cos^k(x)$ where $k$ is odd for skinnier bumps:

Or $sin^{\frac{1}{k}}(x)$ and $cos^{\frac{1}{k}}(x)$ where $k$ is odd for fatter bumps:

Does this suffice for what you are looking for?