Taylor Polynomial for sin(x) at c=0

The Taylor Polynomial of a function is a polynomial that approximates the function at a point [math]c[/math]. This is very useful for transendental functions such as [math]e^x,sin(x),cos(x)[/math], etc...[br][br]The graph below shows 4 degrees of approximation of the function [math]f(x)=A*sin(x)[/math] centered at zero, where [math]A[/math] is a constant. Why is each approximation more accurate than the previous? Does the value of [math]A[/math] affects the graph of the approximations?

Information: Taylor Polynomial for sin(x) at c=0