The discussion centers on the correctness of the procedure for solving the equation A sin(ωt) = A sin(φ). It is established that φ = sin⁻¹(sin(ωt)) is not the appropriate approach, as the oscillatory nature pertains to the sine function rather than the argument φ itself. The correct interpretation is that if sin(ωt) = sin(θ), then θ = ωt + k(2π), where k is an integer. Therefore, φ cannot be simply equated to ωt in terms of oscillation.
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You don't need inverse trig functions here. We can ignore A, assuming that it is a nonzero constant.alejandrito29 said: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 ??