Convert to Polar y=-3

$y = - 3$

Step 1

Since $x = r \cos (θ)$ , replace $x$ with $r \cos (θ)$ .

$y = - 3$

Step 2

Since $y = r \sin (θ)$ , replace $y$ with $r \sin (θ)$ .

$r \sin (θ) = - 3$

Step 3

Divide each term in $r \sin (θ) = - 3$ by $\sin (θ)$ and simplify.

Divide each term in $r \sin (θ) = - 3$ by $\sin (θ)$ .

$\frac{r \sin (θ)}{\sin (θ)} = \frac{- 3}{\sin (θ)}$

Simplify the left side.

Cancel the common factor of $\sin (θ)$ .

Cancel the common factor.

$\frac{r \sin (θ)}{\sin (θ)} = \frac{- 3}{\sin (θ)}$

Divide $r$ by $1$ .

$r = \frac{- 3}{\sin (θ)}$

Simplify the right side.

Separate fractions.

$r = \frac{- 3}{1} \cdot \frac{1}{\sin (θ)}$

Convert from $\frac{1}{\sin (θ)}$ to $\csc (θ)$ .

$r = \frac{- 3}{1} \csc (θ)$

Divide $- 3$ by $1$ .

$r = - 3 \csc (θ)$