Circle Trig

[fading flower]

2sin^2(x-3) sin(x-2)=0 for 0≤x≤2π
what is x?

[spare slate]

divide both sides by 2
sin²(x-3) sin(x-2) = 0
zero factor principle
sin²(x-3) = 0
-> sin(x-3) = 0
-> x-3 = 0, x-3 = pi
-> x = 3, x = pi+3
sin(x-2) = 0
-> x-2 = 0, x-2 = pi
-> x = 2, x = pi+2
x = {2, 3, pi+2, pi+3}

[fading flower]

wha? but the sin(x-2)=0 stays the same

you just divided one of them, which was 2sin squared

[spare slate]

wdym

[fading flower]

wait, but the answer given is 7π/6 and 11π/6

[spare slate]

how come?

[fresh birch]

answer this