Best fit sinusoidal wave in r
The pattern you describe is not obvious, or strong. Nevertheless, to answer your question, use Fourier series like this:

library(forecast)
y &lt;- ts(c(6.62,6.57,6.57,6.55,6.52,6.56,6.52,6.55,6.54,6.55,6.55,6.62,
          6.78,6.73,6.6,6.59,6.57,6.57,6.51,6.55,6.39,6.4,6.15,6.22,
          6.3,6.27,6.27,6.24,6.24,6.23,6.22,6.26,6.23,6.22,6.2,6.14),
        frequency=12)
mylm &lt;- tslm(y ~ trend + fourier(y, K=3))
plot(y, type='p')
lines(fitted(mylm), col='blue')




This is called a harmonic regression. See https://otexts.org/fpp2/useful-predictors.html#fourier-series for the details.