This project will introduce functions.

$($Mandatory$)$ A Taylor series expansion can approximate various functions with its

terms...the more terms, the closer to the real function value it is$.$ The Taylor series

expansion of

$sin(x)={\displaystyle \underset{n=0}{\overset{}{}}}\frac{(-1{)}^n}{(2n+1)!}{x}^{2n+1},$ for all $x$

$cos(x)={\displaystyle \underset{n=0}{\overset{}{}}}\frac{(-1{)}^n}{(2n)!}{x}^{2n},$ for all $x$

Write two functions $($using a new $*.$h and $*.$cpp file$)$

that calculate $sin(x)$ and $cos(x),$ until some term is less than ${10}^{-3}.$ Write a program that

prompts for $x$ and uses your two functions to calculate these values. Print out the result.

Test cases: $sin(0\mathrm{.}5)=0\mathrm{.}479425,cos(0\mathrm{.}5)=0\mathrm{.}87758$;$sin(2)=0\mathrm{.}90929,cos(2)=-0\mathrm{.}41614$

Important! Use the factorial function given in class $($from lecture$)$ to do the

denominators of the above equations.$)$

$($Optional$)$Add a $tan(x)$ function to the first program. You will use the $sin(x)$ and $cos(x)$

functions to implement the $tan(x)$ function $).$

Test cases: $tan(0\mathrm{.}5)=0\mathrm{.}5463$;$tan(2)=-2\mathrm{.}18504$

$($Please use basic c$++$ code$)$

hard$-$coded loops?...not

allowed $($use the method that

the assignment shows, and as

demonstrated in class$)$

remember that you must use

separate files when you make

your own functions....a so$,$ no

header file? $($as repeatedly

discussed in class!