Show that sin(x) = O(x) for all x in R.

From the defn, we must show

s.t.

We know that |sin(x)| <= 1.

But now I'm stuck.

Similarly, how would I go about showing:

s.t.

What's the general method for these things? (I know is always positive, so the mod signs are redundant)

(The above is derived from , m positive integer.)