Answer:
[tex]126\degree[/tex]
and
[tex]126\degree[/tex]
respectively.
Step-by-step explanation:
The given trigonometric equation is
[tex]\sin2x=3\cos2x[/tex]
We divide both sides by [tex]\cos2x[/tex] to get,
[tex]\frac{\sin2x}{\cos2x}=3[/tex]
This implies that,
[tex]\tan2x=3[/tex]
We take the inverse tangent of both sides to get,
[tex]2x=\tan^{-1}(3)[/tex]
[tex]\Rightarrow 2x=71.565[/tex]
[tex]\Rightarrow x=35.7825[/tex]
[tex]\Rightarrow x\approx 36\degree[/tex]
Since the tangent ratio has a period of [tex]180\degree[/tex], another solution is
[tex]x=180+36[/tex]
[tex]x=216\degree[/tex] to the nearest degree.
In the third quadrant,
[tex]2x=180+71.565[/tex]
[tex]\Rightarrow 2x=251.565[/tex]
[tex]\Rightarrow x=125.7825[/tex]
[tex]\Rightarrow x=126\degree[/tex]
The solutions are
[tex]x=36\degree,126\degree,216\degree[/tex]
The value of x that satisfies the equation if x lies in the second quadrant is [tex]126\degree[/tex]
The value of x that satisfies the equation if x lies in the third quadrant is[tex]216\degree[/tex]
