why sin(x) is different to sqrt(1-cos(x).^2)

Question

Luis Isaac 2015-12-30

回答： Walter Roberson 2015-12-30

Dear, I'm new at matlab programming

I do not undestand why the following results s and s2 are different:

teta=0:pi/10:2*pi;
s=sin(teta);
s2=sqrt(1-cos(teta).^2);
sum(abs(s-s2))

The answer is

ans =

12.6275

But I think that the result should be 0 because sin(x)=sqrt(1-cos(x)^2) Why am I wrong?, where is my mistake?

Sorry for this question and thanks in advance

Luis Isaac 2015-12-30

Sorry for the question: The answer is the absolute value: sqrt(x^2)~=x and sqrt(x^2)==abs(x)!!!

Answer 1

Walter Roberson 2015-12-30

sum(sin(teta).^2 + cos(teta).^2 -1) is 0 to within roundoff error.

What you are missing is the adjustment for sign, because sqrt() returns the positive square root only