I need some help finding the solutions for: 4sin^2(x)-3=0?

Answer 1

The last answer is not complete at all.

4sin^2(x)-3 =0 <=> sin^2(x)= 3/4
<=> sin(x) = sqrt(3) /2 or sin (x) = -sqrt(3)/2

first:
sin(x) = sqrt(3) /2 <==> sin(x) =sin (pi/3)
<==> x = pi/3 [2pi] or x=pi-pi/3=2*pi/3 [2pi]

second:
sin(x) = -sqrt(3) /2 <==> sin(x) =sin (-pi/3)
<==> x = -pi/3 [2pi] or x=-pi+pi/3=-2*pi/3 [2pi]

so there are 4 solutions:

x = pi/3 +k*(2*pi) or
x = 2pi/3 +k*(2*pi) or
x = -pi/3 +k*(2*pi) or
x = -2pi/3 +k*(2*pi)

(k is of course an integer)

Answer 2

4sin^2(x) - 3 = 0
sin^2(x) = 3/4
sin x = (3^0.5) / 2
x = 60 degree
-