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"#