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

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

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.

Charismaztex

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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].