Hi,

I want to calculate how much time will my circuit be able to work on a 9V battery (565mAh), knowing that the current characteristics looks like that:

The current is show using the green color. It's peak is about 28mA.

Could you please show me how I can calculate it?

 

You are probably interested in the average current.

For a sine wave, average = 0.64 peak. Since you are only using half the cycle, the average current is 0.32 x peak, or 9 ma in your case.

You can use a discharge curve for the particular type of battery you are using to estimate the battery life.

The chart below is a sample of a set of discharge curves:

 

Bear in mind that it is generally unwise to completely flatten a battery.
In addition, Murphy's Law dictates that actual battery life is always less than the theoretical value .