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

$246$

cos $1$

$2!4!6!$

x x x

x $=-+-+$

Write an algorithm to implement this formula so that it computes and prints out the values of cos x as each

term in the series is added. In other words, compute and print in sequence the values for

$2$

$24$

cos $1$

cos $1$

$2!$

cos $1$

$2!4!$

x

x

x

x x

x

$=$

$=-$

$=-+$

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

error as

true series approximation

$\%$ error $100\%$

true

$-$

$=$

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

The development of the algorithm hinges on recognizing that the series approximation of the sine can be

represented concisely by the summation,