How do you find an equivalent equation in rectangular coordinates #r = 1 + 2 sin x#?

Question

20458 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-08T13:38:36

#x^2+y^2=sqrt(x^2+y^2)+2y#

The relation between polar coordinates #(r,theta)# and rectangular coordinates #(x,y)# is

#x=rcostheta# and #y=rsintheta# i.e. #x^2+y^2=r^2#

Hence, we can write #r=1+2sinx#

as #sqrt(x^2+y^2)=1+(2y)/sqrt(x^2+y^2)#

or #x^2+y^2=sqrt(x^2+y^2)+2y#

The graph appears as follows (drawn using tool from Wolform):

enter image source here