Finding the absolute extrema of $F(x) = 2x + 5\cos(x)$ 
Find the absolute extrema of $F(x) = 2x + 5\cos(x)$ on the interval $[0,2\pi]$ using the extreme value theorem.
Answer should be 2 ordered pairs.

I got $\arcsin(2/5)$ for the first value of $x$, but can’t figure out the second.
Thanks in advance.

Derivative vanishes at $\sin^{-1}\dfrac{2}{5}$
plugin and extreme values are
$$ \sqrt{21} + 2(\sin^{-1}\dfrac{2}{5}+ 2 n \pi) $$
Odd multiples are discarded as they give a minimum, can be checked by sign of second derivative. Only alternate roots are considered for maxima.
and the corresponding x-values (first x- value of pair) are
$$ \sin^{-1}(2/5) + 2 n \pi $$
