$2\mathrm{.}4$ The sine function can be evaluated by the following infinite series:

$cosx=1-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}+$cdots

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

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

$cosx=1$

$cosx=1-\frac{x^2}{2!}$

$cosx=1-\frac{x^2}{2!}+\frac{x^4}{4!}$

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

error as

$\%$ error $=\frac{\text{t}\text{r}\text{u}\text{e}-\text{s}\text{e}\text{r}\text{i}\text{e}\text{s}\text{a}\text{p}\text{p}\text{r}\text{o}\text{x}\text{i}\text{m}\text{a}\text{t}\text{i}\text{o}\text{n}}{\text{t}\text{r}\text{u}\text{e}}*100\%$

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,

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written consent of McGraw$-$Hill Education.

${\displaystyle \underset{i=0}{\overset{n}{}}}(-1{)}^i\frac{x^{2i}}{(2i)!}$

where $i=$ the order of the approximation.

$($a$)$ Structured flowchart?

$($b$)$ Pseudocode?