Period of a polar curve

Main Question or Discussion Point

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..

[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!
 

Answers and Replies

Gib Z
Homework Helper
3,344
4
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.
 
Ok, thanks
 

Related Threads for: Period of a polar curve

  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
1K
Replies
6
Views
1K
Replies
15
Views
1K
Replies
5
Views
900
Replies
2
Views
4K
Top