Trig Equation?

Question

1. 2sin^2 theta + 5 sin theta + 1 = 0

Thanks.

Answer 1

let sin theta equal x.
Now you have the equation 2x^2+5x+1=0
Using the quadratic equation: [-5+-sqrt(25-8)]/4
equals -.219 or -2.28 which is too small to be a solution (since sin takes values only between -1 and 1). Therefore, arcsin(-.219)=-12.65 degrees.

Answer 2

sin @=((-5+-sqrt(25-8))/4.The minus sign gives sin@<-1 impossible
so sin@=-0.3486 and @=5.9346 rad and @=3.4902 rad