Is there a way to retrieve the points where a function like $f(x) = \sqrt x - 5$ intersects with a periodic function like $\sin x$?
With a constant $f(x) = c$, it's easy: when it intersects, there are infinite solutions, by using $\arcsin x$ we can get the angle which produced $c$, and every other solution is a the same interval ($2k\pi$) away from the last.
For some reason, I think the derivative $df(x)/dx$ might be significant.
Edit: To clarify, this can be done using numerical methods or by iterating on points over some range of $x$ and computing their values. However, I'm interested in finding an analytical solution, if it can be done!
Thanks for your help.