Identify the maximum and minimum values of the function y = 10 cos x in the interval [-2π, 2π].

answer if only know

We know that the maximum and minimum values of the function y = cos x in the interval [-2π, 2π] are 1 and -1 respectively.
 
The graph of y = 8 cos x is vertical stretch by a factor of 8 units. Therefore the graph y=cos x, = the maximum and minimum values of the function y = cos x in the interval [-2π, 2π]. So they are 8 and -8 respectively.  

max = 8,  ∈[−2π,2π]
                                                    = Solution 
min = −8.  ∈[−2π,2π]

Maximum values:

(-2 pi, 10), (0, 10),(2 pi, 10),

Minimum values:

(- pi, -10), (pi, -10),

Geometric pattern of 2 i’m guessing. not really sure about what you’re asking but i hope this !