For many students, the measurement of \(\phi\) is the most difficult and most unfamiliar measurement for spherical coordinates. In order to help understand the measurement of the \(\phi\)-coordinate, we will look at the collection of points described by a constant value of \(\phi\text{.}\) For each of the equations below, you should:
Draw a plot of the points that satisfy that equation. For some equations, your plot will be a path in space and others will correspond to a surface. You should draw how the \(\phi\)-coordinate is measured and related to the graph.
Write a sentence or two that describes the shape and features of your plot of the equation. You should mention any other descriptions that could be applied to your set of points, such as axes or coordinate planes.
