# Math Help - LIMITS and CONTINUITY !!!!

1. ## LIMITS and CONTINUITY !!!!

prove that cosine is a continuous function!!

how do you prove that it is continuous using limit laws?

2. ## Re: LIMITS and CONTINUITY !!!!

In this thread you are supposed to prove that sine is continuous. Cosine can be expressed through sine. Or use the same method as for sine.

3. ## Re: LIMITS and CONTINUITY !!!!

Originally Posted by pnfuller
prove that cosine is a continuous function!!
how do you prove that it is continuous using limit laws?
Show that ${\lim _{h \to 0}}\cos \left( {x + h} \right) = \cos (x)$

4. ## Re: LIMITS and CONTINUITY !!!!

and how do you do that?

5. ## Re: LIMITS and CONTINUITY !!!!

Prove that sin(x) and cos(x) are continuous at x= 0, first. Then use the fact that cos(x+y)= cos(x)cos(y)- sin(x)sin(y). How you prove that sin(x) and cos(x) are continuous at x= 0 depends on precisely how you have defined sine and cosine.