How do you measure the duty cycle of sinus with a arduino uno?

Sinus waves are not to be sniffed at.

On the other hand sin waves can be measured. But as has been pointed out they have a 50% duty cycle.
A duty cycle is the ratio of on to off time which in a sin wave can be considered as the positive and negative parts of the cycle.

However a quick google of the term
arduino frequency measurement
gives plenty of examples.