Question

Find all solutions in the interval [0, 2π).

4 sin2 x - 4 sin x + 1 = 0

Answer 1

its basically a quadratic equation that can be factorised

(2sin(x) -1)^2 = 0

so you need to solve

2sin(x) -1 = 0

consider the domain when looking for solutions.. as there are 2 answers.

Answer 2

so sin x = 1/2?
I'm still confused as to how you got there...

Answer 3

@campbell_st

Answer 4

let t= sinx , so you have sin^2x = t^2, right? replace to the equation, you have
4t^2 -4t +1=0, solve for t, then plug back to t = sinx , solve for x , don't forget interval

Answer 5

Oh! That makes sense. Thank you!