Chapter 2, Problem 4P

The sine function can be evaluated by the following infinite series:

$\text{sin }x=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+$…

Write an algorithm to implement this formula so that it computes and prints out the values of sin x as each term in the series is added. In other words, compute and print in sequence the values for

$\begin{array}{l}\text{sin }x=x\\ \text{sin }x=x-\frac{x^3}{3!}\\ \text{sin }x=x-\frac{x^3}{3!}+\frac{x^5}{5!}\end{array}$

up to the order term n of your choosing. For each of the preceding, compute and display the percent relative error as

$\%\text{error = }\frac{\text{true}-\text{series approximation}}{\text{true}}\times 10\%$

Write the algorithm as (a) a structured flowchart and (b) pseudocode.