Question

convert the equation to polar form. (use variables r and θ as needed.) y = 6

Explanation:

Step1: Recall polar coordinate conversion

We know that in polar coordinates, \( y = r\sin\theta \).

Step2: Substitute into the equation

Given the equation \( y = 6 \), substitute \( y = r\sin\theta \) into it. So we get \( r\sin\theta=6 \). Then, solve for \( r \) (if needed, but the polar form can also be left as \( r\sin\theta = 6 \) or solved for \( r \) as \( r=\frac{6}{\sin\theta} \), which can also be written as \( r = 6\csc\theta \) since \( \csc\theta=\frac{1}{\sin\theta} \)).

Answer:

\( r\sin\theta = 6 \) (or \( r = \frac{6}{\sin\theta} \) or \( r = 6\csc\theta \))