Graphs of equations in polar coordinates

Example 1: A circle of radius 1

Equation of the graph: \,\,\,\,\, r(\theta) = 1, \,\,\,\,\, 0\leq \theta \leq 2 \pi.
This is the the graph of the equation $r(\theta)$

The variable $\theta$

Example 2: A circle of radius 1/2 centered at (1/2,0)

$$r(\theta) = cos\, \theta, \,\,\,\,\, 0\leq \theta \leq \pi$$
The graph of $r(\theta) = cos (\theta)$

The graph of $cos (\theta), \,\,\,\,\, 0\leq \theta \leq \,\pi$

Example 3: A flower with four petals.

$$r(\theta) = cos\, (2 \,\theta), \,\,\,\,\, 0\leq \theta \leq 2\,\pi$$
The graph of $r(\theta) = cos (2 \theta)$

The graph of $cos ( \theta),\,\,\,\,\,0\leq \theta \leq 2\,\pi$

Example 4: A flower with three petals.

$$r(\theta) = cos\,( 3 \,\theta), \,\,\,\,\, 0\leq \theta \leq \,\pi$$
The graph of $r(\theta) = cos (3 \theta)$

The graph of $cos ( \theta),\,\,\,\,\,0\leq \theta \leq \,\pi$

Example 5: An carcoid

$$r(\theta) = 1- cos( \theta), \,\,\,\,\, 0\leq \theta \leq \, 2\,\pi$$
The graph of $r(\theta) = 1- cos (\theta)$

The graph of $1-cos ( \theta),\,\,\,\,\,0\leq \theta \leq \,2\pi$

Example 6: Another carcoid

$$r(\theta) = 1+ cos( \theta), \,\,\,\,\, 0\leq \theta \leq \, 2\,\pi$$
The graph of $r(\theta) = 1+ cos (\theta)$

The graph of $1+cos ( \theta),\,\,\,\,\,0\leq \theta \leq \,2\pi$