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

Create an M-file to implement this formula so that it computes and displays the values of sin x as each term in the series is added. In other words, compute and display in sequence the values for

sin x = x

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

As a test case, employ the program to compute sin(0.9) for up to and including eight terms—that is, up to the term x¹⁵/15!.

sin.x = x x + 3! 5!