Chapter 9, Problem 44CLT

To determine

To plot: the given point in polar coordinates and find three additional polar representations of the point.

Answer to Problem 44CLT

  $\left(5,\frac{3\pi }{2}\right),\left(-5,\frac{\pi }{2}\right),\left(-5,-\frac{3\pi }{2}\right)$

Explanation of Solution

Given:

The point $\left(5,-\frac{\pi }{2}\right)$ .

Calculation:

For the given point $\left(5,-\frac{\pi }{2}\right)$ , $r=5$ and $\theta =-\frac{\pi }{2}$ . The point can be plotted on polar coordinates as shown below.

  

Now, add $2\pi$ to get anotherrepresentation of the point as $\left(5,-\frac{\pi }{2}+2\pi \right)=\left(5,\frac{3\pi }{2}\right)$ .

Change the signs of the coordinates to get the second representation of the point as $\left(-5,\frac{\pi }{2}\right)$ .

Now, subtract $2\pi$ from $\frac{\pi }{2}$ to get the third representation of the point as $\left(-5,\frac{\pi }{2}-2\pi \right)=\left(-5,-\frac{3\pi }{2}\right)$ .

Thus, the additional three representations are $\left(5,\frac{3\pi }{2}\right),\left(-5,\frac{\pi }{2}\right)$ and $\left(-5,-\frac{3\pi }{2}\right)$ .