Chapter 4, Problem 24P

Develop a well-structured program to compute the Maclaurin series expansion for the cosine function as described in Prob. 4.2. The function should have the following features:

• Iterate until the relative error falls below a stopping criterion $\left(\text{es}\right)$ or exceeds a maximum number of iterations $\left(\text{maxit}\right)$. Allow the user to specify values for these parameters.

• Include default values of $\left(\text{es}\right)$ $\text{es}\left(=0.000001\right)\text{ and maxit}\left(=100\right)$ in the event that they are not specified by the user.

• Return the estimate of $\cos \left(x\right)$, the approximate relative error, the number of iterations, and the true relative error (that you can calculate based on the built-in cosine function).