find the solutions of the equation that are in the interval [0,2pi). 2cos^2 y+ cos y = 0

Answer 1

Let x = cosy

then

2x^2 + x = 0

x(2x+1) = 0

x= 0, -1/2 = cosy

the angle whose cosine is 0 is 90 degrees = pi/2

the angle whose cosine is -1/2 is 120 degrees or pi/3

those are the only solutions in the 1st and 2nd quadrants, between angles 0 to 2pi