# Prove that cos:R->[-1,1] is continuous at every a∈R

1. Mar 15, 2010

### Charismaztex

Prove that cos:R-->[-1,1] is continuous at every a∈R

1. The problem statement, all variables and given/known data

Prove that cos:R-->[-1,1] is continuous at every a∈R

2. Relevant equations

N/A

3. The attempt at a solution

If the function is right continuous at -1, and left continuous at 1, then should the function be continuous in the interval? so the limit of cos(x) as it approaches -1 from the right towards -1 should be the same as cos(-1), and vice versa for the other side. Please confirm or deny this.

Thanks in advance,
Charismaztex

Last edited: Mar 15, 2010
2. Mar 15, 2010

### mrbohn1

Re: Prove that cos:R-->[-1,1] is continuous at every a∈R

I think you may have your domain and your range confused: you need to show that cos is continuous at every point in $$\mathbb{R}$$, not just in the interval: [-1,1].

I suggest using a delta/epsilon argument...

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