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: [tex]\left|[/tex]sin a -sin b [tex]\right|[/tex] [tex]\leq[/tex] [tex]\left|[/tex] a - b[tex]\right|[/tex] 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.