Question

In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.

$\theta =\mathrm{\pi }$

Short answer

The required equation is$y=0$.

Step-by-step solution

Step 1. Given information.

The given equation in polar coordinates is:

$\theta =\mathrm{\pi }$

Step 2. Find the equation in rectangular coordinates.

Use the formula $\tan \theta =\frac{y}{x}$,

$$\begin{gathered} \tan \mathrm{\pi }=\frac{y}{x} \\ 0=\frac{y}{x}\left[\mathrm{Since}\mathrm{tan\pi }=0\right] \\ y=0 \end{gathered}$$

Therefore, the equation in rectangular coordinates is$y=0$.