Chapter 9, Problem 16RE

To determine

To write:the polar equation of the rectangular coordinates $\left(x,y\right)$ of the given variables $r\text{ and }\theta$ . Also, identify the equation and graph it.

Answer to Problem 16RE

The equation of the straight line is $x=y$ .

Explanation of Solution

Given:

The givenequation is $\theta =\frac{\pi }{4}$ .

Calculation:

As it is known that $x=r\cos \theta y=r\sin \theta$ .

  $\begin{array}{l}x=r\cos \theta =r\cos \frac{\pi }{4}=\frac{r}{\sqrt{2}}\\ y=r\sin \theta =r\sin \frac{\pi }{4}=\frac{r}{\sqrt{2}}\\ \therefore x=y\end{array}$ .

From above, it is found that the above equation $x=y$ is the equation of straight line.

Now, draw the graph of the circle.

  

Hence, polar equation of the rectangular coordinates is $x=y$ .