(Solved): In Exercises 1-12, sketch the graph described by the following cylindrical coordinates in three-di ...

In Exercises 1-12, sketch the graph described by the following cylindrical coordinates in three-dimensional space. 1. \( r=2 \) 2. \( \theta=\frac{\pi}{4} \) 3. \( z=-1 \) 4. \( z=r \) 5. \( r=\theta \) 6. \( z=r \sin \theta \) 7. \( r^{2}+z^{2}=4 \) 8. \( 1 \leq r \leq 2, \quad 0 \leq \theta \leq \frac{\pi}{3} \) 9. \( r \leq z \leq \sqrt{9-r^{2}} \) 10. \( 0 \leq r \leq 2 \sin \theta, \quad 1 \leq z \leq 3 \) 11. \( 0 \leq r \leq 4 \cos \theta, \quad 0 \leq \theta \leq \frac{\pi}{2}, \quad 0 \leq z \leq 5 \) 12. \( 0 \leq r \leq 3, \quad \frac{-\pi}{2} \leq \theta \leq \frac{\pi}{2}, \quad 0 \leq z \leq r \cos \theta \)