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

Explanation

(i) `(2,pi//3)-=(r,theta)`
We have ` x=rcostheta=2"cos"(pi)/(3)=2xx(1)/(2)=1`
and `y=rsintheta=2"sin"(pi)/(3)=2xxsqrt(3)/(2)=sqrt(3)`
Therefore, the point is `(1,sqrt(3)` in the Cartesian coordinates.
(iii) `x=-sqrt(2) "cos"(pi)/(4)=-sqrt(2)((1)/(sqrt2))=-1`
`y=-sqrt(2)"sin"(pi)/(4) =-sqrt(2)((1)/(sqrt2))=-1`
So, the equivalent Cartesian coordinates for the given polar coordinates are `(-1,-1)`.