What are some examples that require the use of Sinusoidal Regression? I am interested in knowing where do regression models of the form:
$$
\phi(x,A,B,C)=A\sin(kx+B)+C
$$
for a given $k\in\mathbb{R}$ are applied in domains such as engineering and science. What example are there that requires the use of this model?
I had encountered this model recently on math stack exchange. I would suspect the use of this model would be in a domain that heavily requires the use of signal processing but I can't seem to find any answer on the web of any application of sine regression.
These questions on MATHSE are mainly about how to transform the nonlinear sine model to a linear one via substitution in order to be solved numerically (such as using the normal system)
https://math.stackexchange.com/questions/3926007/least-squares-regression-of-sine-wave
https://math.stackexchange.com/questions/2368821/find-a-sinusoidal-regression-equation-for-some-given-data

Harmonic regression is your term. There's an equivalent and possibly easier form to deal with: $A\sin \omega t+B\cos \omega t+c$. This is also called a regression with Fourier predictors.
This is used anywhere where you expect constant wave like pattern in data, e.g. seasonality in sales revenues or prices. You often use more than one harmonic though, e.g. $ \omega t,2 \omega t,\dots$ to reproduce more complex patterns than a perfect sine wave
