Question

Confusion about inequalities in trigonometry.
f(x)=-2cosx+1
a)Solve for f(x)=0
b)Solve for f(x)>0
c)Solve for f(x)<0

a) Is easy. f(x)=pi/3 and 5pi/3
b) and c) is where I get messed up.

Our teacher has us graph the cos (x) graph and then the line y=1/2 and find the two intersections. I thought anything over the intersections was considered greater than 0 and anything below the intersections on the graph was less than 0. The book says the opposite but I think the book maybe wrong? Someone please explain?