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Worksheet Practice Graphs with Spherical Coordinates
1.
In each of the following cases, the spherical coordinates \((\rho,\theta, \phi)\) of a point in space are given. Draw the point \(P\) in three-dimensional space by identifying the angles \(\theta\) and \(\phi\) and the distance \(\rho\) in your drawing.
\(\displaystyle (2,\frac{\pi}{3},\frac{\pi}{4})\)
\(\displaystyle (3,\frac{3\pi}{2},\frac{3\pi}{4})\)
\(\rho =2\) and \(\phi = \pi\)
\(\displaystyle (2,0,\frac{\pi}{2})\)
2.
In each of the following cases draw the region of three-dimensional space that is described by the given description in cylindrical coordinates.
\(0\leq \rho \leq 2\text{,}\) \(0\leq \phi \leq \frac{\pi}{4}\)
\(1\leq \rho \leq 2\text{,}\) \(\pi\leq \theta \leq \frac{3\pi}{2}\)
\(0\leq \rho \leq 2\text{,}\) \(\frac{\pi}{2}\leq \theta \leq \pi\text{,}\) \(0\leq \phi \leq \frac{\pi}{2}\)
\(1\leq \rho \leq 2\text{,}\) \(\frac{\pi}{4}\leq \theta \leq \frac{3\pi}{4}\text{,}\) \(\frac{\pi}{2}\leq \phi \leq \pi\)
\(0\leq \rho \leq 3\text{,}\) \(\pi\leq \theta \leq \frac{3\pi}{2}\text{,}\) \(\frac{\pi}{4}\leq \phi \leq \pi\)
