Question

Find all solutions of the equation in the interval [0, 2Ï€).
2 sin^2 θ - 3 sin θ - 2 = 0

Answer 1

use quadratic formula, taking a=2, b=3, c=-2. when getting theta, keep in mind the interval and reject the values which are not in it

Answer 2

* b=-3

Answer 3

Call sin x = x. Solve the quadratic equation
2x^2 - 3x - 2 = 0
D = b^2 - 4ac = 9 + 16 = 25 -> VD = 5
x1 = 3/4 + 5/4 = 2 , rejected because > 1
x2 = 3/4 - 5/4 = -2/4 = -1/2
sin x = -1/2 = sin (-Pi/6) or = sin 7Pi/6 or sin 11Pi/6
x = 7Pi/6 , and x = 11Pi/6