How do you sketch the graph of the polar equation and find the tangents at the pole of #r=3sintheta#?

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Answer 1 · 2017-11-17T14:28:29

#theta=0#

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

The equation #r=3sintheta# can be written as #r^2=3rsintheta#

i.e. #x^2+y^2=3y# which can be modified as

#x^2+(y-3/2)^2=(3/2)^2#

which is equation of a circle with center at #(0,3/2)# and radius #3/2#. Its graph is as shown below.

graph{x^2+y^2=3y [-5, 5, -1, 4]}

and tangent at pole i.e. #(0,0)# is #y=0#,

which in polar form is #theta=0#