Question

Given f: R->[-1,+1]: x->cos(x)
Show f(x) is continuous in its domain with the use of epsilon delta definition

Answer 1

this is not that easy i think
it depends also on your definition of cosine
first you prove it is continuous at say 0 and then you prove
\[\lim_{h\to 0}\cos(x+h)=\cos(x)\] probably using "addition angle" formula

Answer 2

you will need a geometric argument, try page 5 and 6 here

Answer 3

addition angle formula? simpsons formulas?