Question

Which, if any, of A. (4, π/6), B. (−4, 7π/6), C. (4, 13π/6), are polar coordinates for the point given in Cartesian coordinates by P(2, 2 √ 3)?

Answer 1

Answer:

The polar coordinates of $}\left(2,\:2\sqrt{3}\right)$ are $\left(4,\:\frac{\pi }{3}\right)$.

Step-by-step explanation:

To convert Cartesian coordinates $\:\left(x,\:y\right)$ to Polar coordinates $\:\left(r,\:\theta \right)$ apply:

$r=\sqrt{x^2+y^2}\quad \theta =\arctan \left(\frac{y}{x}\right)$

$x=2\\\\y=2\sqrt{3}$

$r=\sqrt{x^2+y^2}\\r=\sqrt{2^2+\left(2\sqrt{3}\right)^2}\\r=4$

$\theta =\arctan \left(\frac{y}{x}\right)\\\theta=\arctan \left(\frac{2\sqrt{3}}{2}\right)\\\theta=\frac{\pi }{3}$

The polar coordinates of $}\left(2,\:2\sqrt{3}\right)$ are $\left(4,\:\frac{\pi }{3}\right)$.