Use inverse functions where needed to find all solutions of the equation in the interval [0,2n)

Question

Use inverse functions where needed to find all solutions of the equation in the interval [0,2n)

csc^2 x-7 csc x=0

Answer 1

csc^2(x) - 7cscx = 0 factor to get:

cscx(cscx-7) = 0 set each factor =0

cscx = 0 cosecants are either greater than 1 or less than -1 but never inbetween

cscx = 0 has no solution

cscx =7

1/sinx = 7

sinx = 1/7

x = about 8.2 degrees

or also 180-8.2 = 171.8 degrees