If the function is:

f(x)=2cos(x)-1 [0,2pi]
A) What are the intervalos of concacity?
B) What are the inflection pinta

My answers:
A) concave down: [0,pi/2) and (3pi/2, 2pi]
concave up: (pi/2, 3pi/2)
B) inflection points:
(pi/2, -1)
(3pi/2, -1)

Please check if these are right if not could it be explained why. I think I'm struggling because it is a trig function so I cant understand....

your answers are correct.

I assumed you correctly noted that f"(x) = -2cosx