Question

Given cscx =-5/2 between 270 and 360 find sin2x

Answer 1

Hello :
cscx = -5/2
1/sinx =-5/2
sinx=-2/5
sin²x+cos²x=1
4/25+cos²x=25/25
cos²x = 21/25
between 270 and 360 : cosx > 0 cosx=(√21)/5
but : sin2x =2sinx cosx
sin2x = 2(-2/5)((√21)/5)
sin2x = (-4√21)/25