In Example 3 it is stated that for all x we have | sin x| ≤ |x|. Use the following to verify this statement.
a. Show that for all x ≥ 0we have f (x) = x−sin x is non-decreasing, which implies that sin x ≤ x with equality only when x = 0.
b. Use the fact that the sine function is odd to reach the conclusion.