Find the solutions of the equation that are...

Question

Find the solutions of the equation that are in the interval [0, 2π). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

 

2 sin² u = −1 − 3 sin u

Answer 1

2 sin² u = -1 - 3 sin u

2 sin² u + 3 sin u + 1 = 0

(2 sin u + 1)(sin u + 1) = 0

 

sin u = -1

u = 5Π/4

 

or

 

2 sin u + 1 = 0

2 sin u = -1

sin u = -1/2     reference angle is π/6, angles are in Q III and Q IV.

u ∈ {7π/6, 11π/6}