How do I prove $\sin x$ is uniformly continuous on $\mathbb R$ with delta and epsilon?
I proved geometrically that $\sin x<x$ and thus, $$|f(x_1)-f(x_2)|=|\sin x_1 - \sin x_2|\le|\sin x_1|+|\sin x_2|<|x_1|+|x_2|$$
But this doesn't help me much finding a delta...
Thanks for any help!
P.S. I'm only at the beginning of calculus so I can't use many theorems and derivation (because they haven't been regorously proven).