Q 53. - Calculus

Question

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

$y=-3$

Step-by-Step Solution

Answer

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

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 $\sin \theta$,

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

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