Don't feel stupid!! Stupid people don't ask questions 🙂 Just think of a circle. A circle is 360 degrees. So think of an angle that is like 300 degrees. It is 300 degrees around a circle so 60 degrees shy of a full circle. Therefore, the cosine of 60 degrees will be the cosine of 300 degrees.
I believe the technical term for this is "reference angle." It will work for any angle.
The only thing you need to be careful of with this is positive/negative signs. For 300 degrees you are in the 4th quadrant and cosine is positive. But if you are in the 2nd or 3rd quadrants the cosine is negative.
