In each of the following cases, the cylindrical coordinates \((r,\theta,z)\) of a point in space are given. Draw the point \(P\) in three-dimensional space by identifying the angle \(\theta\) and the distance \(r\) in your drawing.
\(\displaystyle (2,\frac{\pi}{3},4)\)
\(\displaystyle (1,\pi,-1)\)
2.
In each of the following cases draw the region of three-dimensional space that is described by the given description in cylindrical coordinates.
\(r=1\) (include a written description as well)
\(\theta=\frac{\pi}{2}\) (include a written description as well)
\(0\leq r \leq 2\text{,}\)\(0\leq \theta \leq \frac{\pi}{2}\)
\(0\leq r \leq 2\text{,}\)\(z=4\)
\(0\leq \theta \leq \frac{\pi}{2}\text{,}\)\(0\leq z \)
\(2\leq r \leq 3\text{,}\)\(\frac{\pi}{2} \leq \theta \leq \pi \text{,}\)\(0\leq z \leq 1\)
