Questions: Rewrite the Cartesian equation x=-2 as a polar equation. r(θ)=

Transcript text: Rewrite the Cartesian equation $x=-2$ as a polar equation. \[ r(\theta)= \]

Solution

Solution Steps

Step 1: Substitute Cartesian Coordinates

We start with the Cartesian equation $ x = -2 $. In polar coordinates, we have the relationship $ x = r \cos(\theta) $. Therefore, we can rewrite the equation as: \[ r \cos(\theta) = -2 \]

Step 2: Solve for $ r $

To isolate $ r $, we rearrange the equation: \[ r = \frac{-2}{\cos(\theta)} \]

Step 3: Final Polar Equation

Thus, the polar equation corresponding to the Cartesian equation $ x = -2 $ is: \[ r(\theta) = \frac{-2}{\cos(\theta)} \]

Final Answer

$\boxed{r(\theta) = \frac{-2}{\cos(\theta)}}$

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