You solution is correct.
I do have one question: "why convert to degrees"?
Radians are mathematical, not degrees. (My opinion)
My question is:
4sin(x)^2 + 7sin(x) = 2
Here is what I did:
4sin(x)^2 + 7sin(x) -2 = 0
(4sinx - 1)(1sinx + 2) = 0
4sinx -1 = 0 or Sinx +2 =0
sinx = (1/4) Sinx = -2
I multiplied both sides of each equation by the inverse of sin resulting in:
Sinx = (1/4) at 0.25 radians - (14.48 degrees) in quadrant one, and 104.47 degrees in quadrant two (90 degrees + 14.48 = 104.48 degrees)
Sinx = -2 is not possible - no solution.
My professor has never used obscure degrees like this before, so I'm wondering if I'm doing something wrong. Any suggestions?
Thanks in advance!