Question

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

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

Answer 1

Suppose cos x = y

Answer 2

Suppose cos theta = x

2x^2 - 3x + 1 = 0

Answer 3

continuing from @saifoo.khan factor that polynomial out by using product sum method or any other method you are good with so from that our product is 2 and sum is -3 we get -2 and -1 so now we have 2x^2 -2x -x +1 = 2x(x-1) -(x-1) = (2x-1)(x-1) = 0

so now we have 2x-1=0 and x-1=0 and from their x=1/2 or x=1

and now sub our cos back into x to get cos theta =1/2 and costheta =1

Answer 4

now to get solutions for costheta = 1 we can draw our cos graph and see that occurs when theta = 0 and theta = 2pi

Answer 5

now we look at for cos theta = 1/2 and now we will use our graph and see when that occurs alright by applying special triangle so let me draw that for you