How do you convert #r=7sintheta# into rectangular equations?

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Answer 1 · 2016-09-16T16:00:31

#x^2+y^2-7y=0#

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

#x=rcostheta#, #y=rsintheta# i.e. #x=r/costheta#, #y=r/sintheta# and #r^2=x^2+y^2#,

Hence #r=7sintheta# can be written as

#r=7sintheta# (multiplying both sides by #r#) or

#r^2=7rsintheta# or

#x^2+y^2=7y# or

#x^2+y^2-7y=0#

graph{x^2+y^2-7y=0 [-10.29, 9.71, -1.48, 8.52]}