What kind of a polar graph is #r=19sin2x#?

1 Answer
Feb 23, 2016

Graph is a continuous finite curve which looks like two petals in first and third quadrant.

Explanation:

Let us convert the polar graph is #r=19sin2x# (we are assuming #theta# has been written as #x# in this equation) in Cartesian coordinates #(x,y)#. As relation between two is given by #r^2=x^2+y^2#, #rcostheta=x# and #rsintheta=y#. Let us eliminate #r# and #theta# using these,

#r=19sin2theta# can be written as #r=19*2sinthetacostheta# or

#r=19*2*y/r*x/r# or #r^3=38xy# or #(r^2)^1.5=38xy#

# graph{(x^2+y^2)^1.5=38xy [-18.02, 18.03, -9.01, 9.01]} #

As is seen, graph is a continuous finite curve which looks like two petals in first and third quadrant.