Question

Find the value of x in the interval (-π, 0) where the graph of the function f(x) = x+2sin(x) has a horizontal tangent line.

Answer 1

a horizontal tangent line means that the derivative of the function at that point is 0.
so find f'(x) and set it to 0

Answer 2

and find the values of x that makes f'(x)=0 in the interval (-pi, 0)

Answer 3

the derivative is 2cos(x)+1. when I equal that to zero it is cos(x)=-1/2. whats the next step?