Question

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

Answer 1

`(4,pi/6)`

Explanation:

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

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

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

and `color(red)(bar(ul(|color(white)(2/2)color(black)(theta=tan^-1(y/x))color(white)(2/2)|)))`

`"here " x=2sqrt3" and " y=2`

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

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

`theta=tan^-1(2/(2sqrt3))=tan^-1(1/sqrt3)=pi/6`

and `pi/6" is the reference angle in the first quadrant"`

`rArr(2sqrt3,2)to(4,pi/6)`