period of this signal
You are mostly correct.  The equation should be $w(t) = sin(2\pi\frac{1}{20}t)$.  The variable in the sin should be $t$, not $f$.  The frequency is determined by the $\frac{1}{20}$, not by the variable.

Other than that you are correct.  The period is 20s, which makes it a $\frac{1}{20}$ Hz sin wave.