Autocorrelation of discrete signal $\sin{2\pi fn}$
well, there's an old trig identity that you learned pre-calculus:

$$ \sin(\alpha + \beta) = \sin(\alpha)\cos(\beta) + \cos(\alpha)\sin(\beta) $$

or, alternatively

$$ \sin(\alpha) \sin(\beta) = \tfrac12 \big(\cos(\alpha-\beta) - \cos(\alpha+\beta)\big) $$

and you will need to use one of those.

but you have a bigger problem because $x[n] = \sin(2\pi f n)$ is a finite power, infinite energy signal.  the definition for autocorrelation is different, i believe for power signals than for energy signals.

the equation for crosscorrelation for power signals is, i believe,

$$ r_{xy}[m] \ = \ \lim_{N \to \infty} \ \ \tfrac{1}{2N+1} \sum_{n=-N}^{N}x[n] \overline{y[n-m]} $$

for autocorrelation of a purely real signal

$$ r_{xx}[m] \ = \ \lim_{N \to \infty} \ \ \tfrac{1}{2N+1} \sum_{n=-N}^{N}x[n] x[n-m] $$