# Period of a polar curve

1. Apr 2, 2008

### 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!

2. Apr 2, 2008

### 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.

3. Apr 2, 2008

Ok, thanks