Question

In Problems 1–3, plot each point given in polar coordinates, and find its rectangular coordinates:

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

Short answer

The rectangular co-ordinates of the polar co-ordinate $\left(-3,-\frac{\pi }{2}\right)$are $(0,3)$and the graph is

Step-by-step solution

Step 1. Given Information  

We are given the polar co-ordinates as $\left(-3,-\frac{\pi }{2}\right)$

Comparing it with standard polar co-ordinates $(r,\theta )$, we get,

$$\begin{gathered} r=-3, \\ \theta =-\frac{\pi }{2} \end{gathered}$$

Step 2. Plotting the polar co-ordinate  

Since the angle is $\frac{-\pi }{2}$, we will make the angle between the axis and the line as $\frac{-\pi }{2}$Also the length is given as $r=-3$(Opposite direction)

Step 3. Rectangular co-ordinates.  

We know, the relation between polar and rectangular co-ordinates is,

$x=r\cos \theta \text{and}y=r\sin \theta$

Thus the value is

$$\begin{gathered} x=-3.\cos (-\frac{\pi }{2}) \\ x=0 \\ y=-3.\sin (-\frac{\pi }{2}) \\ y=-3.-1 \\ y=3 \end{gathered}$$

Thus, the point will be$(0,3)$