Question

How do you convert the rectangular coordinate `(1,-sqrt3)` into polar coordinates?

Answer 1

`rec(1,-sqrt3)=` `pol(2,-pi/3)` in radians or `pol(2,-60^@)` in degrees

Explanation:

Polar in in the form `(r,theta)`

`r=sqrt(x^2+y^2)`

and

`theta=tan^-1(y/x)`

`:.` `(r, theta)=` `(sqrt(1^2+(-sqrt(3))),tan^-1((-sqrt(3))/1))`

`=(sqrt(4),-pi/3)`

`=(2,-pi/3)`

Convert radians to degrees by `180/pi`

`=(2,-cancel(pi)/3*180/cancel(pi))`

`=(2,-180/3)`

`=(2,-60^@)`

`=(2,300^@)`