How do you change the rectangular coordinate #(-6, 6sqrt3)# into polar coordinates?
1 Answer
Aug 25, 2016
Explanation:
To convert from
#color(blue)"rectangular to polar coordinates"# That is
#(x,y)to(r,theta)#
#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 = - 6 and y
#=6sqrt3#
#rArrr=sqrt(6^2+(6sqrt3)^2)=sqrt(36+108)=sqrt144=12# Now
#(-6,6sqrt3)# is in the 2nd quadrant so we must ensure that#theta# is in the 2nd quadrant.
#theta=tan^-1((6sqrt3)/-6)=tan^-1(-sqrt3)#
#=-pi/3" in 4th quadrant"#
#rArrtheta=(pi-pi/3)=(2pi)/3" in 2nd quadrant"#
#rArr(-6,6sqrt3)to(12,(2pi)/3)#