CalcVR Supplemental Materials

In the first lesson on spherical coordinates in three dimensions, the measurements of the \(\rho\text{,}\) \(\theta\text{,}\) and \(\phi\) coordinates are introduced. Several examples are given showing the geometric measurements for each coordinate. Since \(\phi\) is measured in a different way than previous coordinates, there is a focus on the measurement of this coordinate. The activity below follows up with a brief exploration on coordinate measurements and graphs of equations. The wire frame grid of spherical coordinates is also shown and related to ideas on a globe. Specifically, the ideas of poles, equator, latitude, and longitude are introduced are briefly related to spherical coordinates. There are numerous questions about measurement of spherical coordinates related to curves in space and octants.

In the second lesson on spherical coordinates in three dimensions, the surfaces created by a fixed value of \(\rho\text{,}\) \(\theta\text{,}\) and \(\phi\) are explored. There are several questions and examples dealing with the possible shapes given by constant values of \(\phi\text{.}\) There are also questions about the spherical coordinates related to inequalities and regions in space.