Question

Q7 Q16.) Convert the polar equation to a rectangular equation.

Answer 1

In polar coordinates, we have

$x=r\cos\theta\implies\cos\theta=\dfrac xr$
$y=r\sin\theta\implies\sin\theta=\dfrac yr$

From this we can write

$\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac{\frac yr}{\frac xr}=\dfrac yx$

If $\theta=\dfrac{4\pi}3$, then $\tan\theta=\sqrt$, so we get

$\dfrac yx=\sqrt3\implies y=\sqrt3\,x$