How do you convert the rectangular point #(2,2sqrt3)# into polar form?
1 Answer
Oct 5, 2016
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"#