Question

In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.
$r=6\csc \theta$

Short answer

The required equation is$y=6$.

Step-by-step solution

Step 1. Given information.

The given equation in polar coordinates is:

$r=6\csc \theta$

Step 2. Find the equation in rectangular coordinates.

$$\begin{gathered} r=6\csc \theta \\ r=6·\frac{1}{\sin \theta } \\ r\sin \theta =6 \\ y=6\left[\mathrm{Since}r\sin \theta =y\right] \end{gathered}$$

Therefore, the equation in rectangular coordinates is$y=6$.