How do you find the rectangular coordinates given the polar coordinates $(-2,(4pi)/3)$ ?

Question

5173 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-21T10:49:08

The rectangular coordinates are $=(1,-sqrt3)$

To convert from polar coordinates $(r,theta)$ to recangular coordinates $(x,y)$

We use the following

$x=rcostheta$

and $y=rsintheta$

Here, $(r,theta)= (-2,(4pi)/3)$

$:. x=-2cos((4pi)/3)$

and $y=-2sin((4pi)/3)$

$cos((4pi)/3)=-1/2$ and $sin((4pi)/3)=sqrt3/2$

Therefore, $(x,y)=(1,-sqrt3)$

How do you find the rectangular coordinates given the polar coordinates (-2,(4pi)/3)(-2,(4pi)/3)?