Yup!
Correct again!
Though note that periodic models like this have inherently multimodal likelihoods when attempting inference on the frequency, which is not particularly compatible with HMC-style samplers as used by Stan. If you have good prior information on the frequency you might be able to use this to isolate the peak, but if not you might need to try some of the reparameterizations in the thread I linked or a different sampler.