#include

#include

$//$ Function Prototypes

double calculate$\_$exp$($double x$,$ int t$)$;

double calculate$\_$sin$($double x$,$ int t$)$;

double factorial$($int n$)$;

$//$ Main Function

int main$()\{$

$//$ Program header

printf$("$Author: Your Name

$")$;

printf$("$Class: Your Class

$")$;

printf$("$Date: Today's Date

$")$;

printf$("$Description: This program evaluates exponential and sine functions using power series.

$")$;

char option;

double x$,$ result, math$\_$h$,$ error;

int t;

$//$ Display the menu

printf$("$Please select an option:

$")$;

printf$("$a$)$ Evaluate exp function

$")$;

printf$("$b$)$ Evaluate sin function

$")$;

$//$ Get the user's choice

scanf$("\%$c$",$ &option$)$;

if $($option $==\text{'}$a$\text{'}||$ option $==\text{'}$A$\text{'})\{$

printf$("$Valid option

$")$;

$//$ Get user inputs for x and t

printf$("$Enter the value for x: $")$;

scanf$("\%$lf$",$ &x$)$;

printf$("$Enter the number of terms t: $")$;

scanf$("\%$d$",$ &t$)$;

$//$ Calculate exp using power series

result $=$ calculate$\_$exp$($x$,$ t$)$;

$//$ Calculate exp using math.h

math$\_$h $=$ exp$($x$)$;

$//$ Calculate the percentage error

error $=$ fabs$(($result $-$ math$\_$h$)/$ math$\_$h $*100)$;

$//$ Display the result

printf$("\%4\mathrm{.}1$lf $\%4$d $\%6\mathrm{.}4$lf $\%6\mathrm{.}4$lf $\%6\mathrm{.}4$lf

$",$ x$,$ t$,$ result, math$\_$h$,$ error$)$;

$\}$ else if $($option $==\text{'}$b$\text{'}||$ option $==\text{'}$B$\text{'})\{$

printf$("$Valid option

$")$;

$//$ Get user inputs for x and t

printf$("$Enter the value for x: $")$;

scanf$("\%$lf$",$ &x$)$;

printf$("$Enter the number of terms t: $")$;

scanf$("\%$d$",$ &t$)$;

$//$ Calculate sin using power series

result $=$ calculate$\_$sin$($x$,$ t$)$;

$//$ Calculate sin using math.h

math$\_$h $=$ sin$($x$)$;

$//$ Calculate the percentage error

error $=$ fabs$(($result $-$ math$\_$h$)/$ math$\_$h $*100)$;

$//$ Display the result

printf$("\%4\mathrm{.}1$lf $\%4$d $\%6\mathrm{.}4$lf $\%6\mathrm{.}4$lf $\%6\mathrm{.}4$lf

$",$ x$,$ t$,$ result, math$\_$h$,$ error$)$;

$\}$ else $\{$

printf$("$Invalid option

$")$;

$\}$

return $0$;

$\}$

$//$ Function Definitions

double calculate$\_$exp$($double x$,$ int t$)\{$

double sum $=1\mathrm{.}0$; $//$ Start with $1($x$^0/0!)$

for $($int n $=1$; n $<$ t; $++$n$)\{$

sum $+=$ pow$($x$,$ n$)/$ factorial$($n$)$;

$\}$

return sum;

$\}$

double calculate$\_$sin$($double x$,$ int t$)\{$

double sum $=0\mathrm{.}0$;

for $($int n $=0$; n $<$ t; $++$n$)\{$

int coefficient $=$ pow$(-1,$ n$)$; $//$ Alternate between $+$ and $-$

sum $+=$ coefficient $*$ pow$($x$,2*$n $+1)/$ factorial$(2*$n $+1)$;

$\}$

return sum;

$\}$

double factorial$($int n$)\{$

if $($n $==0)\{$

return $1\mathrm{.}0$;

$\}$

double fact $=1\mathrm{.}0$;

for $($int i $=1$; i $<=$ n; $++$i$)\{$

fact $*=$ i;

$\}$

return fact;

$\}$