Solve the equation. (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians.)

Question

csc²(x) + 8 csc(x) − 9 = 0

Answer 1

csc^2(x) + 8csc(x) - 9=0

let y = csc(x)

then

y^2 + 8y -9 = 0

(y+9)(y-1) = 0

y = 1, -9

csc(x) = 1 = 1/sin(x)

sin(x) = 1, x=arcsin(1) = 90 degrees + 360n where n= any integer

or csc(x)=-9

= 1/sin(x)

sin(x)= -1/9 = about -6.38 degrees, 353.62 degrees or 186.38 degrees plus 360n where n = any integer

x = pi/2, about 1.96pi, about 1.04pi radians plus 2npi where n = any integer

x= pi/2+2npi, 1.96pi+2npi, 1.04pi+2npi