# How do you convert r = 4csc(x) into cartesian form?

Jan 24, 2017

Assuming the equation was $r = 4 \csc \theta$, the rectangular form is $y = 4$.

#### Explanation:

(Assuming that the equation you meant is $r = 4 \csc \theta$, since polar equations use $r$ and $\theta$.)

When converting from polar to rectangular, it's important to know that:

• $x = r \cos \theta$
• $y = r \sin \theta$

The equation can be rewritten using $\csc \theta = \frac{1}{\sin} \theta$ and then multiplying both sides by $\sin \theta$:

$r = 4 \csc \theta \text{ "=>" "r=4/sintheta" "=>" } r \sin \theta = 4$

With the identity from before:

$y = 4$

which is a horizontal line.