This is a two part question, and I need help with the 2nd part.
For this 1st question, I found the remainder term and showed that for $0 < c < \pi$, the remainder term is $> 0$, therefore, the inequality holds true. Is this sufficient proof?
The 2nd part of the question asks:
Show that the inequality in part (1) holds for all real positive x and deduce that:
$x-\frac{x^3}{6} < \sin x < x$
for all real positive $x$.
Can someone help me with this second part?
Thanks in advance!