> Also is the Sandwich theorem only really used with sine > and cosine? If not does anyone have some other good examples.
Let f be the function defined by f(x) = 0 if x is rational and f(x) = 1 if x is irrational. Note that f is discontinuous at every point. In fact, at every point f has neither a left limit nor a right limit.
Now define the function g by putting g(x) = x*f(x).
Using the Sandwich Theorem, you can show that g is continuous at x = 0. It's also easy to show that g is not continuous at every other point, so g has the property that it's continuous at exactly one point.