What is the Equation for Tangents to a Polar Curve at the Pole?

[lovelylila]

Find the Cartesian equations of the tangent lines at the pole of r=sin2theta.* I know to set r=sin2theta equal to zero. This means that theta can equal 0, pi/2, pi, 3pi/2, 2pi. Now I also know to plug each of these theta values into the equation for slope of a polar curve, which is:

r'sintheta + rcostheta/ (r'costheta- rsintheta)

r'= 2cos2theta

*So starting with 0, for example, gives you (2)(0) + (0)(1)/ ((2)(1)- (0)(0). This equals 0/2, which means its a horizontal tangents. I get similar results for the other theta values- either horizontal or vertical tangents. Using x=rcostheta for vertical tangents, @ 0 i get x=0 (and similar results for the other values). I'm so confused though- this doesn't make sense, I looked at the polar graph and I can't see how the tangents at the pole are x=0 and y=0! What am I doing wrong? Any help would be very much appreciated! :-)

 

[haruspex]

It is a pity that no sketch of the polar graph was posted. The result looks right to me.

 

[Delta2]

This curve is a flower with 4 petals
https://www.wolframalpha.com/input?i=plot+r=sin(2theta)

 

[haruspex]

This curve is a flower with 4 petals
https://www.wolframalpha.com/input?i=plot+r=sin(2theta)

Yes, but what was the OP's sketch? If that's what the OP got, why the objection to the solutions obtained?

 

[Delta2]

Hm, yes weird, the solutions x=0 and y=0 come from the equation for slope he writes.