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

1 Answer
Mar 8, 2018

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

Explanation:

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):

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