Question

Solve 2sin^2 x - 5sin x - 3 = 0.
What is the general formula for all of the solutions?

Answer 1

this is a quadratic equation so uses your skills with solving quadratics.

(2sin(x) + 1)(sin(x) - 3) = 0

sin(x) = -1/2 or 3

the only solution to consider is sin(x) = -1/2 (sin(30) = 1/2)

since sin is negative the solution is in the 3rd and 4th quadrants


then x = 210 or 330 degrees