So I need to apply the Fourier transform to an equation I derived through regression, which is of the form $A\sin(Bt+C)+D$, where $A$, $B$ (or $\omega_0$), $C$ and $D$ are constants.
The method I want to use is converting the function to exponents using Euler's formula and then use the duality property and frequency shifting property. In the case of an equation that is of the form $\sin(\omega_0 t)$, the exponential form of the equation would be
$(e^{i\omega_0 t} - e^{-i\omega_0 t})/2i$
and the Fourier transform using the two properties would be
$(\pi\delta(\omega-\omega_0)-\pi\delta(\omega+\omega_0 ))/i$
I haven't formally been taught the Fourier transform so I might have some basics wrong (I need to do a university level math research paper for high school) but I don't understand how I can apply the method above (for the form $\sin(\omega_0 t)$) to the form $\sin(\omega_0 t + C)$ ($C$ is a constant). How do I do that?