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I usually go from 0 to 2pi but that sometimes get me into trouble.

For example:

Question says find the horizontal and vertical tangents of this curve..

[tex] r=3cos\theta [/tex]

I was like well.. you have horizontal tangents when

[tex] \theta = \pi/2, 3\pi/2, 5\pi/2, 7\pi/2 [/tex]

vertical tangets when

[tex] \theta = 0, \pi/2, \pi, 3\pi/2 [/tex]

until I looked at the solution manual and they have only first half of these points.. then I realized that the curve repeats itself at pi, not 2pi. So yeah any tricks to see when it ends? Thanks!