Chapter 9, Problem 6CT

To determine

The rectangular equation of polar equation $\tan \theta =3$ and graph the equation.

Answer to Problem 6CT

Solution:

The rectangular equation of polar equation $\tan \theta =3$ is $y=3x$ .

The graph of polar equation $\tan \theta =3$ is,

  

Explanation of Solution

Given information:

The polar equation, $\tan \theta =3$

Consider the equation $\tan \theta =3$ ,

In polar coordinates $x=r\cos \theta ,y=r\sin \theta$ and $r^2=x^2+y^2$ .

Thus, $\tan \theta =\frac{y}{x}$ .

Given that, $\tan \theta =3$ ,

  $\Rightarrow 3=\frac{y}{x}$ .

  $\Rightarrow y=3x$

Therefore, the equation in rectangular coordinates is $y=3x$ .

Above equation is an equation of straight line passing through origin having slope $3$ .

The graph of $\tan \theta =3$ is,