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

[Charismaztex]

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

Homework Statement

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

Homework Equations

N/A

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

 

[mrbohn1]

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...