Question

Solve the equation sin2x = 3cos2x. The value of x that satisfies the equation if x lies in the second quadrant is °. The value of x that satisfies the equation if x lies in the third quadrant is °.

Answer 1

Answer:

$126\degree$

and

$126\degree$

respectively.

Step-by-step explanation:

The given trigonometric equation is

$\sin2x=3\cos2x$

We divide both sides by $\cos2x$ to get,

$\frac{\sin2x}{\cos2x}=3$

This implies that,

$\tan2x=3$

We take the inverse tangent of both sides to get,

$2x=\tan^{-1}(3)$

$\Rightarrow 2x=71.565$

$\Rightarrow x=35.7825$

$\Rightarrow x\approx 36\degree$

Since the tangent ratio has a period of $180\degree$, another solution is

$x=180+36$

$x=216\degree$ to the nearest degree.

In the third quadrant,

$2x=180+71.565$

$\Rightarrow 2x=251.565$

$\Rightarrow x=125.7825$

$\Rightarrow x=126\degree$

The solutions are

$x=36\degree,126\degree,216\degree$

The value of x that satisfies the equation if x lies in the second quadrant is $126\degree$

The value of x that satisfies the equation if x lies in the third quadrant is$216\degree$