A little clarification on absolute values

[relinquished™]

Hello again. I have a (stupid, but I'm not real sure about the answer-type) question. I'm trying to prove that the second order ODE of the simple pendulum y''=-(g/l)sin y is Lipschitz (using norm 1). After doing some evaluating, I came up with

$|u'-v'| + |\frac{g}{l}||\sin u - \sin v|$

All I'm asking is if this is true for all values of u and v:

$|\sin u - \sin v| \leq |u - v|$

All clarifications are appreciated.

Thanks,

Reli~

 

[Benny]

I think you can show that |sin(u)-sin(v)| <= |u-v| using the MVT.