Question

need help with the very last part:

Answer 1

i'll post my solution to the earlier bits:

Answer 2

\[f(x) = \sin^2x + 2cosx +1\]
\[f'(x) = 2sinxcosx - 2sinx = 2sinx(cosx - 1)\]
stationary points at:
\[(0,3) , (\pi , -1) , (2 \pi , 3)\]

also we have symmetry, considering each term:
\[f(2 \pi - x) = f(x)\]

so something like this: