Polar, Cylindrical, and Spherical Coordinates

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 unde…

1. Write a couple of sentences describing the graph of $r=c$, where $c$ is a constant. You should consider what values of $c$ will correspond to different shapes.

2. Write a couple of sentences describing the graph of $\theta=d$, where $d$ is a constant. You should consider what values of $d$ will correspond to different shapes.

In this activity, we graph some surfaces using cylindrical coordinates. To improve your intuition and test your understanding, you should first think about what each graph should look like before you plot it using appropriate technology.

1. What familiar surface is described by the points in cylindrical coordinates with $r=2$, $0 \leq \theta \leq 2\pi$, and $0 \leq z \leq 2$? How does this example suggest that we call these coordinates cylindri…