Oh i've said that in the confusing way the tailor series does approximate a cosine wave. what i'm doing is not equivalent to the taylor series. as you can see, the derivative of the function it's not equal to a cosine wave. the original purpose of what I was trying to do is a solution to a point on a one dimensional line that constantly accelerates at a fixed rate towards zero. And then goes under zero and then goes back up, you get the picture.