Convert the following polar coordinates to its equivalent Cartesian coordinates.
(i) `(2,pi)`
(ii) `(sqrt(3),pi//6)`

Answer

(i) `(-2,0)`
(ii) `(3//2,sqrt3//2)`

Explanation

`(i) (2,pi)-=(r,theta)`
`therefore x=rcostheta=2cospi=-2`
and `y=rsintheta =2cospi=-2`
Therefore, the rectangular coordinates are `(x,y)-=(-2,0)`.
`(ii) (sqrt(3),(pi)/(6))-=(r,theta)`
`therefore x=sqrt(3)(pi)/(6)=sqrt(3) (sqrt(3)/(2))=(3)/(2)`
and `y=sqrt(3)sin.(pi)/(6)=sqrt(3)(1)/(2)=(sqrt3)/(2)`