Question

Find all solutions of the equation in the interval [0, 2 Pi)

2 cos^2 theta - 3 cos theta + 1 = 0

Answer 1

D=9-8=1 => cosT=(3+1)/4=1 or cosT=(3-1)/4=1/2
=> T=0, T=60, 300 (degrees)

Answer 2

Hmmm, I got theta=0, pi/6, 5pi/6, and 2 pi, would that be correct?

Answer 3

pi/6=30. cos30=sqrt3/2. 5pi/6=150. cos150<0! 2pi not in the interval [0;2pi)

Answer 4

if you want the answer in the degrees, it's:
0, pi/3, 5pi/3

Answer 5

try to factor first
\[2\cos^2\theta--3\cos \theta+1=0~~this~ gives\\ (\cos \theta-1)(2\cos \theta -1) = 0\\cos \theta=1~~or\\cos \theta=1/2\\so ~~\theta=0,\frac{ \pi }{ 3 },\frac{ 5 \pi }{ 3 }\]