[SPLIT] how to sovle for x in sin2x= -1/3 where pi<x<3pi/2

[csrlock]

how to sovle for x in sin2x= -1/3 where pi<x<3pi/2

find
sin(X)
cot x
cos 4x
tan 4x
csc(2x + 130degrees)
cos 6x


please help me

 

[Ishuda]

how to sovle for x in sin2x= -1/3 where pi<x<3pi/2
...

Something seems wrong to me. If $\displaystyle \pi$ < x < $\displaystyle \frac{3}{2}\pi$, then $\displaystyle 2\pi$ < 2x < $\displaystyle 3\pi$ and the sine is positive in that region.

So how could sin(2x) = -$\displaystyle \frac{1}{3}$ AND $\displaystyle \pi$ < x < $\displaystyle \frac{3}{2}\pi$?