Question

In Exercises 48–55 convert the equations given in rectangular coordinates to equations in polar coordinates.

$y=-3$

Short answer

The required equation is$-3\csc \theta$.

Step-by-step solution

Step 1. Given information.

The given equation in rectangular coordinates is:

$y=-3$

Step 2. Find the equation in rectangular coordinates.

$y=-3$

As we know that in polar coordinates $y=r\sin \theta$, then substitute the value of y ,

$r\sin \theta =-3$

Divide both sides by role="math" localid="1649349326734" $\sin \theta$,

$$\begin{gathered} \frac{r\sin \theta }{\sin \theta }=\frac{-3}{\sin \theta } \\ r=\frac{-3}{\sin \theta } \\ r=-3\csc \theta \end{gathered}$$

Therefore, the equation in polar coordinates is$-3\csc \theta$.