Question

How do you convert the rectangular point `(-3,3sqrt3)` into polar form?

Answer 1

`(6,-pi/3)`

Explanation:

To convert from `color(blue)"rectangular to polar form"`

That is `(x,y)to(r,theta)`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(r=sqrt(x^2+y^2))color(white)(a/a)|)))`

and `color(red)(bar(ul(|color(white)(a/a)color(black)(theta=tan^-1(y/x))color(white)(a/a)|)))`

here x = - 3 and `y=3sqrt3`

`rArrr=sqrt((-3)^2+(3sqrt3)^2)=sqrt(9+27)=sqrt36=6`

Now,`(-3,3sqrt3)` is in the 4th quadrant so we must ensure that `theta` is in the 4th quadrant.

`theta=tan^-1((3sqrt3)/(-3))=tan^-1(-sqrt3)`

`=-pi/3larr" in 4th quadrant"`

Thus `(-3,3sqrt3)to(6,-pi/3)to(6,-60^@)`