Trig Equation: Is This Procedure Correct?

[alejandrito29]

Is correct the following procediment?

$A \sin (\omega t) = A \sin (\phi) \to \phi= \sin^{-1} \sin (\omega t )$

Is correct to say that $\phi = \omega t$ is oscillatory in this case ??

 

[Mark44]

Is correct the following procediment?

$A \sin (\omega t) = A \sin (\phi) \to \phi= \sin^{-1} \sin (\omega t )$

Is correct to say that $\phi = \omega t$ is oscillatory in this case ??

You don't need inverse trig functions here. We can ignore A, assuming that it is a nonzero constant.
If sin(ωt) = sin(θ), then θ = ωt + k($2\pi$), where k is an integer.

 

[HallsofIvy]

But you certainly cannot "say that \phi= \omega t is oscillatory"! It is the function sin(\phi) that is oscillatory, not just the argument, \phi.