Glen_b and I have been debating how to edit this particular question. My view is that a title specific to the contents of the question is necessary as a summary of the question contents. The title, as I edited it, allows one to quickly understand that the question is about using trig functions in regression without venturing further than the "headline."
On the other hand, Glen_b's title is less descriptive of the question body than mine. Its generality may have merit, though, as it can include several types of transformations for regression analysis under its aegis. Rather than face an avalanche of questions asking "how do I apply __ transform in my regression," we might use this question to capture many transformations at once.
I do not think that Glen_b's approach is desirable.
- Imprecise question titles are a pet peeve of mine, as it requires one to read the question body to discern whether the result is relevant to what I'm after. This peeve may not have wide appeal, in which case I'll accept that I'm an outlier.
- Collecting all transformations used in regressions into a single question, which is itself about just trig, seems like a very larger task, especially if we admit every transformation satisfying the title "Linear regression with transformed $x$ values." This would appear to include $\log(x)$ and $\log(x+c)$ for some small $c$ (since we need to account for $x$ values which may be 0), $\sqrt{x}$, polynomials, and splines. I'm not sure whether or not the title admits things like Gaussian processes.
- While I appreciate that Glen_b is forward-looking in his attempt to service future users, I'm not sure that expanding OP's question does a great service to OP. OP asked about one specific transformation and may be overwhelmed by a very expansive response.
(I hope that Glen_b finds my summary of his position fair & accurate; he and other CV members are, of course, welcome to make their own cases one way or the other -- my intention in describing his argument is merely expository.)