Question

What is the polar equation of the horizontal line \(y=5 ?\)

Short answer

The polar equation of the horizontal line with the Cartesian equation y=5 is r = 5/sin(θ).

Step-by-step solution

Write down the given equation in Cartesian coordinates

The horizontal line is given by the Cartesian equation \(y=5\).

Replace \(y\) with its polar equivalent

As mentioned in the analysis, we use \(y = r \sin 𝜃\). Substituting this into our equation, we get \(r \sin 𝜃 = 5\).

Solve for \(r\)

To isolate \(r\), we can divide both sides of the equation by \(\sin 𝜃\). So, \(r = \frac{5}{\sin 𝜃}\).

Final Answer: The polar equation of the horizontal line

The polar equation of the horizontal line \(y=5\) is given by \(r = \frac{5}{\sin 𝜃}\).