sin A = 1/2 and cos A = 1/3.

Hence, A = π/ 6 and 0

So, A = π/ 6 and cos^-1(0) > B >cos^-1(1/2)

how?????

your question is wrong either sinA=1/2 or cosA=1/3 because if sinA=1/2 for sure cosA=root 3/2 (positive or negative)
check your question and respost it