Answer:
The solutions are π/4, 3π/4,5π/4,7π/4
Step-by-step explanation:
The given equation is
6sin²(x) = 3
Divide by 6 to get:
[tex] { \sin}^{2} (x) = \frac{1}{2} [/tex]
This implies that;
[tex] \sin(x) = \pm \frac{ \sqrt{2} }{2} [/tex]
If
[tex]\sin(x) = \frac{ \sqrt{2} }{2}[/tex]
[tex]x = \frac{\pi}{4} [/tex]
in the first quadrant
[tex]x = \frac{3\pi}{4} [/tex]
in the second quadrant.
If
[tex]\sin(x) = - \frac{ \sqrt{2} }{2}[/tex]
[tex]x = \frac{5\pi}{4} [/tex]
in the third quadrant
[tex]x = \frac{7\pi}{4} [/tex]
