Chapter 9, Problem 3CT

To determine

To graph: The point $\left(-4,\frac{\pi }{3}\right)$ in the polar coordinates.

Explanation of Solution

Given information:

The point, $\left(-4,\frac{\pi }{3}\right)$

Graph:

The point in a polar coordinate system is represented by an order pair $\left(r,\theta \right)$ .

Here the point is $\left(-4,\frac{\pi }{3}\right)$ .

Thus, $r=-4,\theta =\frac{\pi }{3}$ .

So the angle between the terminal side and initial side is $\frac{\pi }{3}$ and the point has length of $4$ units in negative direction from the origin as shown below,

  

Interpretation:

From the figure, the point lies in third quadrant.