Activity 9.9.4

Below are several equations, some in polar form and some in rectangular form. For each equation, complete the following steps:

1. Convert the equation to the other coordinate system (either rectangular to polar or polar to rectangular).
2. State the shape of the graph for the equation and any other information needed to graph
3. Graph the given equation and write a sentence explaining how the graph helps understand the converted equation you found in the first step.

1. $r=2$

2. $\theta=\frac{\pi}{3}$

3. $x=-1$

4. $y=2$

5. $y=-x$

6. $r=\displaystyle\frac{3}{1-2\cos(\theta)}$