How does one determine the period of a polar curve?

[motornoob101]

How does one know when the a polar curve repeats itself?

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..

$$r=3cos\theta$$

I was like well.. you have horizontal tangents when

$$\theta = \pi/2, 3\pi/2, 5\pi/2, 7\pi/2$$

vertical tangets when

$$\theta = 0, \pi/2, \pi, 3\pi/2$$

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!

 

[Gib Z]

Well graphing it may help, or otherwise; at theta = pi, the line will be going in the negative direction, but cos (pi) is negative 1, so it will start going positive again, ie it starts again.

 

[motornoob101]

Ok, thanks