Q 39. - Calculus

Question

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

Step-by-Step Solution

Answer

The required equation is $y=6$.

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 $y=6$.