Chapter 9.1, Problem 36AYU

In Problems 33-40, plot each point given in polar coordinates, and find other polar coordinates $\left(r,\theta \right)$ of the point for which:

a. $r\text{ > 0, }-2\pi \le \theta \text{ < 0}$

b. $r\text{ < 0, }0\le \theta \text{ < 2}\pi$

c. $r\text{ > 0, }2\pi \le \theta \text{ < 4}\pi$

$\left(2,\pi \right)$

To determine

To plot: Each point given in polar coordinates and find other polar coordinates $\left(r,\theta \right)$ of the point for which:

a. $r>0,-2\pi \le \theta <0$

Answer to Problem 36AYU

a.

Explanation of Solution

Given:

$\left(2,\pi \right)$

Graph:

Calculation:

The point $\left(2,\pi \right)$ is plotted in the graph:

a. Subtract $\left(2\pi \text{radians}\right)$ from the angle $\pi$ to get $\text{P }=\left(2,\pi -2\pi \right)=\left(2,-\pi \right)$.

Graph:

a.

To determine

To plot: Each point given in polar coordinates and find other polar coordinates $\left(r,\theta \right)$ of the point for which:

b. $r<0,0\le \theta <2\pi$

Answer to Problem 36AYU

b.

Explanation of Solution

Given:

$\left(2,\pi \right)$

Graph:

Calculation:

The point $\left(2,\pi \right)$ is plotted in the graph:

b. Subtract $\frac{1}{2}$ revolution $\left(\pi \text{radians}\right)$ to the angle $\pi$, and replace 2 by $-2$ to get $\text{P }=\left(-2,\pi -\pi \right)=\left(-2,0\right)$.

Graph:

b.

To determine

To plot: Each point given in polar coordinates and find other polar coordinates $\left(r,\theta \right)$ of the point for which:

c. $r>0,2\pi \le \theta <4\pi$

Answer to Problem 36AYU

c.

Explanation of Solution

Given:

$\left(2,\pi \right)$

Graph:

Calculation:

The point $\left(2,\pi \right)$ is plotted in the graph:

c. Subtract $\frac{1}{2}$ revolution $\left(\pi \text{radians}\right)$ to the angle $\text{4}\pi$ to get $\text{P }=\left(2,\pi -\pi \right)=\left(2,0\right)$.

Graph:

c.