Taylor Polynomial for sin(x) at c=0

The Taylor Polynomial of a function is a polynomial that approximates the function at a point . The nth Taylor polynomial (or approximation) is given by This is very useful for approximating values of transcendental functions such as , etc... The graph below shows the first four Taylor polynomial approximations of the function centered at zero, where is a constant. Why is each approximation more accurate than the previous one? How does the value of affect the graphs of the approximations?