Trying to get my output to be 22 decimal places

%Murphy Griffin
%ERG280-01
%December 3, 2021
function out=my_sin(x)
xrad=x*pi/180;
sign=1;
n=1;
total=0;
fact=1;
while abs(total-sin(xrad))>=10^(-22)
    if n>200
        break
    end
    total=total+(sign*((xrad^n)/(factorial(fact))));
    fact=fact+2;
    sign=sign*(-1);
    n=n+2;   
end
out=total;
end

I need the output of the fuction to be 22 decimal places but I cant use

digits(22)

vpa(my_sin(73))

to get to 22 decimal places. It needs to occur when I get my answer after inputting my_sin(73)

[Matt J]

It needs to occur when I get my answer after inputting my_sin(73)

What's the difference?

Answer 1

[David Hill]

You cannot use floating point if you want 22 decimal places of accuracy, you must use symbolic.

function total=my_sin(x)
digits(22);
x=sym(num2str(x));
xrad=x*pi/180;
sign=1;
n=1;
total=sym(0);
fact=sym(1);
while abs(total-sin(xrad))>=1e-22
    if n>200
        break
    end
    total=total+(sign*((xrad^n)/(factorial(fact))));
    fact=fact+2;
    sign=sign*(-1);
    n=n+2;   
end
total=vpa(total);
end

[John D'Errico]

+1. But to be picky, for SOME values of x...

sin(0)

ans = 0

really is EXACTLY correct, to even more than 22 decimal places. ;-)