If (for say, visual aesthetics) I would like to plot the graph of a sine wave on a 2D graph that intersects the $x$ axis with value of $y =0$ when $x$ is some arbitrary integer - how would I go about doing that?
Obviously it is trivial to find this function for the initial intersection; I'd like to investigate whether there exists a method to generate a wave that crosses this point after its first period.
To make it clear: I know how to plot the graph, but not how to find the seed value for the function.
Edit - added image: Apologies, I couldn't find a way to word the question for the actual outcome I wanted so tried to get a foothold by finding the intersect as $y =0$. I'm interested in getting all waves that 'peak' at a given value for $x$. I'm struggling a little with the terminology.
If you fix the amplitude and phase, then the waves that first peak at $x = x_0$ are given by:
$$y = \sin \left ( \frac{\pi}{n}\left ( x - x_0 + \frac{n}{2}\right )\right )$$
These have period, amplitude, and phase of $2n$, $1$, and $x_0-\frac{\pi}{2}$, respectively.
Try it out here.