Chapter 14.5, Problem 37E

To determine

Find the polar form.

Answer to Problem 37E

  $\cot \theta =1$

Explanation of Solution

Given information:

Given: $x=y$

Calculation:

Here, we have to find the polar form:

  $\begin{array}{l}r=\sqrt{x^2+y^2}\\ \theta ={\tan }^{-1}\left(\frac{y}{x}\right)\\ x=r\cos \theta \\ y=r\sin \theta \\ Wehave:\\ x=y\\ r\cos \theta =r\sin \theta \\ \cot \theta =1\end{array}$

Hence, the polar form is $\cot \theta =1$ .