Find when two sin graphs hit $x=0$ at the same time Lets say I have 2 sine functions. They could be any sine functions but I'm more interested in the ones that get bigger/smaller as they go.
So we have:
$$
y_1 = \sin{(x^2)}
$$
$$
y_2=\sin{\left(\sqrt{x}\right)}
$$
I'm interested in when they both hit $y=0$ at the same time.
I don't know where to even start.

You have $x^2 = \pi n$ and $\sqrt{x} = \pi m$. Eliminating $x$ gives $n = \pi^3 m^4$. As $\pi$ is irrational $m$ must be 0, and hence $x = 0$ is the only solution.
