Asymmetric periods in a sine curve

I am wondering how to graph an asymmetric sine wave so that the slope of one side of the parabola is larger than the other, much in the same way as a sine graph with decreasing frequency. However I was wondering if there was a method to graph it so that the frequency does not continue to decrease, but is instead the same asymmetric shape throughout.

2 Answers

If you mean that you want a periodic function whose period looks like a "distorted" sine, you can do that by altering the argument to sine. Normally we look at $\sin (t)$, where $t$ increases steadily. But if we alter this slightly, we can take $\sin (s(t))$, where $s(t)$ has a graph that looks like the graph of $t \mapsto t$, but slightly distorted. A good example: $$ t \mapsto \sin ( t + 0.2 \sin t) $$ Graph:

Same idae, but with $0.2$ replaced by $0.5$:

$$\sin\left(x+\frac{1}{2}\sin(x)\right)$$ is an example of the type of curve that you seem to be looking for