Convert to Polar y=6

$y = 6$

Step 1

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

$y = 6$

Step 2

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

$r \sin (θ) = 6$

Step 3

Divide each term in $r \sin (θ) = 6$ by $\sin (θ)$ and simplify.

Divide each term in $r \sin (θ) = 6$ by $\sin (θ)$ .

$\frac{r \sin (θ)}{\sin (θ)} = \frac{6}{\sin (θ)}$

Simplify the left side.

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

Cancel the common factor.

$\frac{r \sin (θ)}{\sin (θ)} = \frac{6}{\sin (θ)}$

Divide $r$ by $1$ .

$r = \frac{6}{\sin (θ)}$

Simplify the right side.

Separate fractions.

$r = \frac{6}{1} \cdot \frac{1}{\sin (θ)}$

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

$r = \frac{6}{1} \csc (θ)$

Divide $6$ by $1$ .

$r = 6 \csc (θ)$