Question

Graphing Polar Equations

Sketch a graph of the polar equation $r\theta =1,\theta >0$ (reciprocal spiral)

Short answer

The graph of the given polar equation is-

Step-by-step solution

Step 1. Given information

A polar equation is given as $r\theta =1,\theta >0$

Step 2. Concept used

For sketching the graph, first, find different values r for different$\theta$. After that, convert them into x and y by using equations-

$\begin{array}{l}x=r\cos \theta \\ y=r\sin \theta \end{array}$

Once we have the points draw a graph by plotting them.

Step 3. Calculation

The polar equation is given as$r\theta =1,\theta >0$,

Let$\theta =0$,

$r\theta =1$

r= undefined

$\begin{array}{l}\theta =1\\ \Rightarrow r=1\end{array}$ ,

$\begin{array}{l}\theta =2\\ \Rightarrow r=0.5\end{array}$,

$\begin{array}{l}\theta =3\\ \Rightarrow r=0.33\end{array}$

Plot the points on graph-