Lipschitz Continuity & Uniform Continuity: Showing sinx & cosx in R

[barksdalemc]

Homework Statement

Show that Lipschitz continutity imples uniform continuity. In particular show that functions sinx and cosx are uniformly continuous in R.

The Attempt at a Solution

I said that if delta=epsilon/k that Lipschitz continuity imples continuity. Now I am stuck as to how to show uniform continuous.

 

[StatusX]

What are the relevant definitions? Note that Lipschitz continuity is a global property of a function, and uniform continuity is the global version of the local property of ordinary continuity, so it should be straightforward to modify your proof for this case (if it doesn't already apply).

 

[HallsofIvy]

As StatusX said, write out the definitions. What is the difference between "continuous" and "uniformly continuous"? (Your "delta=epsilon/k" contains everything you need.)