Chapter 11.11, Problem 1E

(a)

To determine

To find: The Taylor polynomials up to degree 5 for $f\left(x\right)=\sin x$ centered at $a=0$ and graph f and the polynomials.

(b)

To determine

To evaluate: The function f and its polynomials at $x=\frac{\pi }{4},\frac{\pi }{2}\text{ and }\pi$.

(c)

To determine

To explain: The reason on how the Taylor polynomials converges to $f\left(x\right)$.