Understanding the Transition to Solve for t in an Oscillation Function

[Mynona]

I have a cosine function, namely the function for oscillation x=A cos(wt).

I want to separate the t out here, so I can solve for it. My teacher gave the the answer to be t= (arccos (x/a)/2pi)*T, but I can't quite see where he came up with that. Would anyone be as kind as to give me a more elaborate explanation of how this transition was made.


(2pi and T comes from w=2pi/T).

Sorry for bad English, not a native English speaker obviously :)

 

[Cyosis]

The inverse function of the cosine is the arc cosine. If a function $f(x)$ has an inverse $f^{-1}(x)$ then $f^{-1}(f(x))=f(f^{-1}(x))=x$.

Divide the equation on both sides by A then take the arccos on both sides. Can you calculate $\arccos(\cos(\omega t))$now?