# Thread: Finding Period of polar graph

1. ## Finding Period of polar graph

How come the polar graph of $\displaystyle r=a cos\Theta$ or $\displaystyle r=a sin\Theta$ only has a period of a pi?
To find the period I would use $\displaystyle \frac{2\pi}{b}$, so why wouldnt the period of both these polar circles be$\displaystyle 2\pi$

2. ## Re: Finding Period of polar graph

Originally Posted by delgeezee
How come the polar graph of $\displaystyle r=a cos\Theta$ or $\displaystyle r=a sin\Theta$ only has a period of a pi?
To find the period I would use $\displaystyle \frac{2\pi}{b}$, so why wouldnt the period of both these polar circles be$\displaystyle 2\pi$
Consider $\displaystyle r = a\cos(\theta)$, which is a circle of radius a/2, centered at a/2. From 0 to pi/2 , $\displaystyle \cos(\theta)$ is positive, so r is positive. From pi/2 to pi, $\displaystyle \cos(\theta)$ is negative, which makes r negative as well. On a graph, a negative r implies that the line starts from the origin and proceeds in the direction opposite to that which the corresponding angle points to.

So at theta=0, r = a, and theta=pi, r = -a, which are the same point.