I need to find the exact solutions on the interval [0,2pi) for:
2sin^2(x/2) - 3sin(x/2) + 1 = 0
I would start:
(2sin(x/2)-1)(sin(x/2)-1) = 0
sin(x/2)=1/2 and sin(x/2)=1
Ok, what angle has a sin equal to say 1/2
arc sin (1) = x/2
solve for x
do the same technique for the other solution.
so the solution is pi and the other solution would be
arc sin (1/2) = x/2
pi/6 = x/2
is that right?