Verified Answer :

jo53256

the tangent line is vertical

syed514

Use

 y=rsin(theta)
x=rcos(theta)

Take dy/dx

Use the polar curve formula of dy/dx = rcos(theta) + sin(theta) (dr/d(theta)) / -rsin(theta)+cos(theta) (dr/d(theta))
So when your dx=0 you have a vertical tangent line.

Actually for this equations there are a lot of points where it should be vertical

and the horizontal points aren't quite as easy because you have to solve something like

3(cos^2(theta)-sin^2(theta))=0

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