$\%$ Problem $3$

clc

clear

format long g

cos$\_33=$ zeros$(1,5)$;

cos$\_160=$ zeros$(1,5)$;

x$\_1=33*$pi$/180$; is this correct?

x$\_2=160*$pi$/180$;

n$\_$values $=[1,3,5,8,15]$;

for i $=1$:length$($n$\_$values$)$

n $=$ n$\_$values$($i$)$;

cos$\_$val $=0$;

cos$\_$val$2=0$;

for v $=0$:$2$:$(2*$n$)\%$ Start from $0,$ increment by $2$ for cosine series

z $=($x$\_1)^$v$/$factorial$($v$)$;

z$2=($x$\_2)^$v$/$factorial$($v$)$;

if rem$($v$,4)==0\%$ Alter sign based on the power of v

cos$\_$val $=$ cos$\_$val $+$ z;

cos$\_$val$2=$ cos$\_$val$2+$ z$2$;

else

cos$\_$val $=$ cos$\_$val $-$ z;

cos$\_$val$2=$ cos$\_$val$2-$ z$2$;

end

end

cos$\_33($i$)=$ cos$\_$val;

cos$\_160($i$)=$ cos$\_$val$2$;

end

fprintf$(\text{'}$Taylor series expansion of cos$(33$ degrees$)$:

$\text{'})$;

disp$($cos$\_33)$;

fprintf$(\text{'}$

Taylor series expansion of cos$(160$ degrees$)$:

$\text{'})$;

disp$($cos$\_160)$; is this corrct?