Hi, you will see that at x=2 x Pi (= 6.284..) cos(x) has completed one whole cycle; as there are 2*Pi radians in one cycle. There are also 360 degrees in one cycle. Therefore there are 360 / ( 2 x Pi) = 57.295779.... degrees in one radian. Now simply multiply every term in the expansion by 57.3 and you have the result in degrees. Of course it is easier to just use the original expansion and do a single multiply of the result by 57.3.
I hope this helps! Tony S