Determine the set of values of x.

Question

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

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

Enter your answer using interval notation.

 

set: 

Answer 1

cosx is increasing over the intervals

(-pi, 0)U(pi,2pi)

-pi <x <0 and pi<x<2pi

in each interval, cosx increases from -1 to +1

it's increasing where the slope>0, slope = the derivative = (cosx)' = -sinx

-sinx>0 in quadrant 2&3, from x=pi to x=2pi and from x=-pi to x= 0