Question

Find the rectangular coordinates of the point with the polar coordinates ordered pair 7 comma 2 pi divided by 3.

Answer 1

Answer:

$\left(-\dfrac{7}{2},\dfrac{7\sqrt{3}}{2}\right)$.

Step-by-step explanation:

The given point is

$\left(7,\dfrac{2\pi}{3}\right)$

We need to find the rectangular coordinates of the given point.

If a polar coordinate is $(r,\theta)$, then  

$x=r\cos theta$

$y=r\sin theta$

In the given point $\left(7,\dfrac{2\pi}{3}\right)$,

$r=7,\theta=\dfrac{2\pi}{3}$

Now,

$x=7\cos \dfrac{2\pi}{3}$

$x=7\cos \left(\pi-\dfrac{\pi}{3}\right)$

$x=-7\cos \left(\dfrac{\pi}{3}\right)$

$x=-7\left(\dfrac{1}{2}\right)$

$x=-\dfrac{7}{2}$

and,

$y=7\sin \dfrac{2\pi}{3}$

$y=7\sin \left(\pi-\dfrac{\pi}{3}\right)$

$y=7\sin \left(\dfrac{\pi}{3}\right)$

$y=7\left(\dfrac{\sqrt{3}}{2}\right)$

$y=\dfrac{7\sqrt{3}}{2}$

Therefore, the required point is $\left(-\dfrac{7}{2},\dfrac{7\sqrt{3}}{2}\right)$.