Question

In Problems5–7, convert the polar equation to a rectangular equation. Graph the equation.

$\tan \theta =3$

Short answer

The rectangular equation is $y=3x$.

The graph is as follows,

Step-by-step solution

Step 1. Given information  

We are given a polar equation,

$\tan \theta =3$

We have to convert the polar equation to a rectangular equation.

Step 2. Converting the polar equation to rectangular equation 

We know that,

$$\begin{gathered} x=r\cos \theta \text{and} \\ y=r\sin \theta \\ {x}^2+y^2=r^2 \end{gathered}$$

So,

$$\begin{gathered} \tan \theta =3 \\ \frac{y}{x}=3 \\ y=3x \end{gathered}$$

Step 3. Graphing the equation 

The graph is as follows,