Question

How do you convert the rectangular point `(2,2sqrt3)` into polar form?

Answer 1

`(2,2sqrt3)to(4,pi/3)`

Explanation:

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

`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=2" and " y=2sqrt3`

`rArrr=sqrt(2^2+(2sqrt3)^2)=sqrt(4+12)=4`

Now `(2,2sqrt3)` is in the first quadrant so we must ensure that `theta` is in the first quadrant.

`theta=tan^-1((2sqrt3)/2)`

`=tan^-1(sqrt3)=pi/3larr" in first quadrant"`

`rArr(2,2sqrt3)to(4,pi/3)to(4,60^@)" in polar form"`