csc3x1 Find all of the exact solutions to the following equa

csc(3x)=-1

Find all of the exact solutions to the following equation (which are in the interval [0,2pi)

cosec (3x) = -1

1/ sin(3x) = -1

sin(3x) = -1

sin(3x)= -sin (90) ----------------------------------1

[sin is -ve in IIIrd and IV quadrant)

so sin (3x) = sin(180 +90) ( sin(180+@) = - sin@)

sin( 3x) = sin(270)

3x = 270

x = 90

from eq 1:

sin(3x) = -sin(90)

sin(3x) = sin( 360- 90)

sin(3x) = sin(270)

x = 90