Determine the set of values of x where the function y=cos(x) is increasing where −2π < x < 2π.

Question

(Do not include the endpoints of the intervals, and all intervals should be open intervals on all endpoints)

 

I don't really understand the instructions here. This is one of a few extra credit problems that I don't understand (extra credit problems in my class aren't previously covered so I don't know where to begin to solve this problem. Any help is greatly appreciated!

Answer 1

Evaluate f(x) in the given interval.

 

f(-2π) = cos(-2π) = 1

f(-3π/2) = cos(-3π/2) = 0

f(-π) = cos(-π) = -1

f(-π/2) = cos(-π/2) = 0

 

Continue this pattern.  Then compare the f(x) values to see where those values increase and decrease.

 

As you can see so far, the function decreases in the interval (-2π, -π).