A business operates a coin pusher machines at a local gas station. The last day of each month, the business collects and splits profits with the gas station owner then resets the value of coins in the machine to $80.

The average value of coins in USD in the machine can be modeled with the sinusoidal function V_usd =-20cos(4/30t)+100 , where t= number of days since reset.

What is the period of the function? If the business misses collection at the end of May, should they come back at the end of June to collect their profits?