Question

What are the corresponding rectangular coordinates for point Q equals the ordered pair 6 comma 11 times pi over 6 given in polar coordinates?

Answer 1

rectangular coordinates and polar coordinates are related to each other by the following relation

`\begin{cases}x=r\cos \theta \\ y=r\sin \theta\end{cases}`

On polar coordinates, the first coordinate is the radius and the second the angle. Using this information, we have

`(6,(11\pi)/(6))\rightarrow\begin{cases}x=6\cos (11\pi)/(6) \\ y=6\sin (11\pi)/(6)\end{cases}`

Solving thiose expressions, we have

`\begin{cases}x=6\cos (11\pi)/(6)=6\cdot(\frac{\sqrt[]{3}}{2})=3\sqrt[]{3} \\ y=6\sin (11\pi)/(6)=6\cdot(-(1)/(2))=-3\end{cases}`

Then, the coordinates of the point Q are

`(3\sqrt[]{3},-3)`