**1. The problem statement, all variables and given/known data**
Essentially, the question asks to use the mean value theorem(mvt) to prove the inequality: abs(sina - sinb)

abs(a - b) for all a and b

**3. The attempt at a solution**
I do not have a graphing calculator nor can I use one for this problem, so I need to prove that the inequality basically by proof. What I did was to look at the mvt hypotheses: if the function is continous and differetiable on closed and open on interval a,b, respectively. However, the problem I am having is that I am getting thrown off by the absolute values and the fact that I've never used mvt on inequalities. I know the absolute value of the sin will look like a sequence of upside-down cups with vertical tangents between them. Hints most appreciated.