2cos^2(theta) + Sin(theta)=1

Question

I know I have to use the quadratic formula but i'm having trouble after I convert the Cos^2(theta) to (1-Sin^2(theta))

Answer 1

2(1-sin^2 T) + sin T = 1

2 - 2 sin^2 T +sin T - 1 = 0

-2 sin^2 T + sin T +1 = 0

2 sin^2 T - sin T - 1 = 0
let z = sin T

2 z^2 - z - 1 = 0

(2 z +1)(z-1) = 0

z = -1/2 or z = 1

so sin T = -1/2 gives T = 150 deg or -30 deg

sin T = 1 at 90 deg