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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! :-)

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! :-)

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