Chapter 6.3, Problem 165E

The following exercises make use of the functions $S_5(x)=x+\frac{x^3}{6}+\frac{x^5}{120}$ and $C_4(x)=x-\frac{x^2}{2}+\frac{x^2}{24}$ on $[-\pi ,\pi ]$ .

165. [T] Plot cos²x − (C₄(x))2 on $[-\pi ,\pi ]$ . Compare the maximum difference with the square of the Taylor remainder estimate for cos x.