How do you graph # r = 6 sin theta#?

1 Answer
Shwetank Mauria
Dec 12, 2016

In Cartesian plane draw a circle with center at #(0,3)# and radius #3#.

Explanation:

The relation between polar coordinates #(r,theta)# and Cartesian coordinates #(x,y)# is #x=rcostheta#, #y=rsintheta# and #r^2=x^2+y^2#.

We can use this to convert equation in polar coordinates to an equation with Cartesian coordinates.

#r=6sintheta#

#hArrr^2=6rsintheta#

or #x^2+y^2=6y#

or #(x-0)^2+(y^2-6y+9)=9#

or #(x-0)^2+(y-3)^2=9#

This is the equation of a circle with center at #(0,3)# and radius #3# and hence one can draw it accordingly.
graph{x^2+y^2-6y=0 [-10.42, 9.58, -2.24, 7.76]}

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