How can I fit a sine function to a SVR?
Use nonlinear regression: https://en.wikipedia.org/wiki/Nonlinear_regression.  Write down a model, e.g., $f(x) = \sin(\alpha x + \beta)$, and then try to find parameters $\alpha,\beta$ that minimize the regression error (the sum of the squared error at each point; i.e., square of difference between model's prediction and observed value).  You can use gradient descent or other forms of mathematical optimization for that.  If a sin function isn't the right model, you can write down some other model (with some parameters) and use optimization to find the best values for the parameters.