Question

solve the equation on the interval [0, 2pi)

8 sin^2x = -17 sinx - 9

Answer 1

8sin²(x)+17sin(x)+9 = 0

[8sin(x) + 9][sin(x) + 1] = 0
sin(x) = -9/8 or sin(x) = -1

Answer 2

At this point do I take the arcsin of -9/8 and of -1 to find every possible x in the domain?