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

1 Answer
Oct 5, 2016

(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"