[I think this question is more related to math than physics, so I've thought this forum is more approriate for the following question, let me know if it's not the case]
I have this equation (it's the equation of motion of a spring), $$x(t) = x_r + A\cdot\sin(\sqrt{ \frac{k}{m}}\cdot t+\phi)$$
I need to find parameter $t$, and in order to find $t$ I need to find argument of sine, and after that it's only algebra. But the problem is in finding argument of sine. I can't do this way $$\frac{x(t)-x_r}{A} = \arcsin([...])$$ because I don't know $x(t)$, and therefore it's not possible to use inverse trig function of sine, based on my trig knowledge, it's the only way to find argument.