Question

Polar to Rectangular Sketch a graph of the polar equation, and express the equation in rectangular coordinates.

$\theta =5\pi /6$

Short answer

The equation $\theta =\frac{5\pi }{6}$ has rectangular coordinates $y=-\frac{x}{\sqrt{3}}$ . It can be graphed as

Step-by-step solution

Step 1. Given information.

The given polar equation is$\theta =\frac{5\pi }{6}$ .

Step 2. The rectangular coordinate of the equation and graph it.

We will convert the polar equation to rectangular coordinates using the formulas and then graph it.

The given equation is

$\begin{array}{l}\theta =\frac{5\pi }{6}\\ \Rightarrow \tan \theta =\tan \frac{5\pi }{6}\\ \Rightarrow \frac{y}{x}=-\frac{1}{\sqrt{3}}\\ \Rightarrow y=-\frac{x}{\sqrt{3}}\end{array}$

This is the required rectangular coordinate.
We can see that it represents a straight line.

Step 3. It can be graphed as.