How do you convert #r = 2sintheta - costheta# into cartesian form?

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Answer 1 · 2016-06-09T14:59:25

#x^2+y^2-2y+x=0#

The relation between polar coordinates #(r,theta)# and Cartesian coordinates #(x,y)# is given by

#x=rcostheta#, #y=rsintheta# and #r^2=x^2+y^2#

As #r=2sintheta-costheta# can also be written as (by multiplying each term by #r#)

#r^2=2rsintheta-rcostheta# or

#x^2+y^2=2y-x# or

#x^2+y^2-2y+x=0#

This is the equation of a circle whose graph is as given below.

graph{x^2+y^2-2y+x=0 [-2.97, 2.03, -0.23, 2.27]}