Answer
Local Maximum:$(\frac{-\pi}{6} + 2\pi k, 0.577)$
Local Minimum: $(\frac{7\pi}{6} + 2\pi k, -0.577)$
Work Step by Step
Given: $y = \frac{\cos x}{2 + \sin x} $
The question asks for the maximum and minimum values of the function
The gray dots in the graph represent the intercepts of the function and the local minimum and maximum points.
Local Maximum: $(\frac{-\pi}{6}, 0.577)$ $(\frac{11\pi}{6}, 0.577)$
Local Minimum: $(\frac{7\pi}{6}, -0.577)$ $(\frac{19\pi}{6}, -0.577)$
Thus in general, it is $(\frac{-\pi}{6} + 2\pi k, 0.577)$for maximum and $(\frac{7\pi}{6} + 2\pi k, -0.577)$ for the minimum, where k is any integer
