Question

How do you solve `6sin^2x + sinx -1 = 0`?

Answer 1

Call sin x = t. Solve quadratic equation:
f(t) = 6t^2 + t - 1 = 0

`D = d^2 = 1 = 24 = 25 -> d = +- 5`

`t1 = -1/12 + 5/12 = 4/ 12 = 1/3`
`t2 = -1/12 - 5/12 = -6/12 = -1/2`

On trig unit circle:

`sin x = t = 1/3 -> x = 19. 47 and x = 199.47` deg

`sin x = t = -1/2 -> x = (7pi)/6 and x = (11pi)/6`