No, you are right up to the summation, the i value is the exponent on the -1 so if you expand it out it would be: -5+5+-5+5....461 times which is an odd number making the answer to the summation -5 then the negative outside the summation makes it a positive 5.

Im guessing your grade in English was not very good.

Thats just the begining, cos, sin, tan, pythagoras, it will all make way for a wonderful new world of Math. I feel like I am way too old for this site, you must be in middle school or something.

What part of trig are you in?

Surveyors, engineers, physicists, auto designers, the list goes on. The whole basis of calculus uses trigonometry.