1.9 Polar, Cylindrical, and Spherical Coordinates (continued)

Exercises (continued)

Write a couple of sentences describing the graph of $r=c$, where $c$ is a constant. You should consider what values of $c$ will correspond to different shapes.

Write a couple of sentences describing the graph of $\theta=d$, where $d$ is a constant. You should consider what values of $d$ will correspond to different shapes.

Work through this exercise and explain your reasoning step by step.

Graph the points that satisfy $y=x+1$.

On the same axes as in the previous part, graph the points that satisfy $y \geq x+1$.

Graph the points that satisfy the inequality $x^2+y^2 \leq 4$.

Graph the points that satisfy both $x^2+y^2 \leq 4$ and $y \geq x+1$.

Plot the region that corresponds to the polar inequality $1 \leq r \leq 3$. Write a sentence or two to describe this region.

Plot the region that corresponds to the polar inequality $\frac{\pi}{4} \leq \theta \leq \frac{3\pi}{4}$. Write a sentence or two to describe this region.

Plot the region that corresponds to the polar inequalities $1 \leq r \leq 3$ and $\frac{\pi}{4} \leq \theta \leq \frac{3\pi}{4}$. Write a sentence or two to describe this region.

Plot the region that corresponds to the polar inequality $1 \leq r \leq 3 \cos(\theta)$. Write a sentence or two to describe this region.