Answer:
Second quadrant = 120°.
Third quadrant = 210°
Step-by-step explanation:
We are given that:
[tex]sin^2(x) = 3cos^2(x)[/tex]
The following property is known:
[tex]sin^2(x) +cos^2(x)=1\\[/tex]
Combining both expressions:
[tex]sin^2(x) =1-cos^2(x)\\sin^2(x) = 3cos^2(x)\\\\1-cos^2(x) = 3cos^2(x)\\cos^2(x)=\frac{1}{4}\\cos(x)=\pm \frac{1}{2}[/tex]
If x lies in the second quadrant, then cos(x) = -1/2:
[tex]x=cos^{-1}(1/2)\\x=120^o[/tex]
The value of x that satisfies the equation if x lies in the second quadrant is 120°.
If x lies in the third quadrant, then cos(x) = -1/2:
[tex]x=120+90=210^o[/tex]
The value of x that satisfies the equation if x lies in the third quadrant is 210°
