How do you convert #(7sqrt3, -7) # into polar coordinates?
1 Answer
Jul 28, 2016
Explanation:
To convert from
#color(blue)"cartesian 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)|)))#
#color(red)(|bar(ul(color(white)(a/a)color(black)(theta=tan^-1(y/x))color(white)(a/a)|)))# here
#x=7sqrt3" and " y=-7#
#r=sqrt((7sqrt3)^2+(-7)^2)=sqrt(147+49)=sqrt196=14# Now
#(7sqrt3,-7)# is in the 4th quadrant and care must be taken to ensure#theta# is in the 4th quadrant.
#theta=tan^-1(-7/(7sqrt3))=tan^-1(-1/sqrt3)=-pi/6" 4th quadrant"#
#rArr(7sqrt3,-7)=(14,-pi/6)=(14,-30^@)#
