How does one determine the period of a polar curve?

In summary, when dealing with polar curves, it is important to know when the curve repeats itself. This can be determined by graphing the curve or by looking at the value of theta where the curve starts repeating. In the case of r=3cos\theta, the curve repeats itself at pi, not 2pi. Knowing this can help in finding the horizontal and vertical tangents of the curve.
  • #1
motornoob101
45
0
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!
 
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  • #2
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
Ok, thanks
 

1. What is the period of a polar curve?

The period of a polar curve is the distance between two consecutive points on the curve that have the same angle.

2. How is the period of a polar curve calculated?

The period of a polar curve can be calculated using the formula 2π/b, where b is the coefficient of the polar angle.

3. Can the period of a polar curve be negative?

No, the period of a polar curve cannot be negative as it represents a distance and cannot have a negative value.

4. What is the relationship between the period of a polar curve and its graph?

The period of a polar curve is related to the number of petals or lobes in its graph. The number of petals is equal to the number of times the curve completes a full rotation in one period.

5. How does the period affect the shape of a polar curve?

The period determines the length of each petal or lobe in the graph of a polar curve. A longer period will result in a larger and more spread out graph, while a shorter period will result in a smaller and more compact graph.

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