It seems like it's impossible to get the maclaurin series of sinx, cosx, and ln(x+1) to have a series index beginning at n=0. I'm confused because I think I was taught that taylor series supposedly start at n=0. ?
I don't quite understand your confusion. By series index, do you mean the beginning value of the sum. Like for you mean the n=0 part? Please explain your confusion a little more.
Taylor series do always start with n=0 if my above assumption is true. Note that by the formula for generating every term in a Taylor series that when you apply the fact that 0!=1 and that (the 0th derivative of f(x) is f(x)) then you are simply left with f(a), which can be 0 for a lot of things.