Chapter 5, Problem 40P

The Taylor series expansion for sin²x is:

$x^2-\frac{2^3{x}^4}{4!}+\frac{2^5{x}^6}{6!}-\frac{2^5{x}^6}{6!}+\frac{2^7{x}^8}{8!}$

Plot the figure on the right, which shows, for $0\le x\le 4.5$, the plot of the function sin²x and plots of the Taylor series expansion of sin²x with two, three, and five terms. Label the axes and display a legend.