Question

rewrite the cartesian equation x = -4 as a polar equation. r(θ) = enter theta for θ if needed. question help: video

Explanation:

Step1: Recall the relationship between Cartesian and polar coordinates

We know that \(x = r\cos\theta\) in polar - Cartesian conversion.

Step2: Substitute \(x = r\cos\theta\) into the given Cartesian equation

Given \(x=-4\), substituting \(x = r\cos\theta\) gives \(r\cos\theta=-4\).

Step3: Solve for \(r\)

To express \(r\) as a function of \(\theta\), we use the formula \(r=\frac{-4}{\cos\theta}\). Since \(\frac{1}{\cos\theta}=\sec\theta\), we can also write \(r = - 4\sec\theta\).

Answer:

\(r(\theta)=-\frac{4}{\cos\theta}\) or \(r(\theta)=-4\sec\theta\)