Question

Rectangular Equations to Polar Equations

Convert the equation to polar form.$x=y$

Short answer

The polar equation is$\theta =\frac{\pi }{4},\frac{3\pi }{4}$

Step-by-step solution

Step 1. Given information

An equation is given in a rectangular coordinate system as$x=y$

Step 2. Concept used

Substitute the values in the formulae, do calculations and simplify it. Consider a specific range or radius and angle for a particular answer. Otherwise, there are infinite numbers of equations.

Step 3. Calculation

Formulae used,

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

Substitute the values in the formulae,

$\begin{array}{l}\Rightarrow x=y\\ \Rightarrow r\cos \theta =r\sin \theta \\ \Rightarrow \cos \theta =\sin \theta \\ \Rightarrow \tan \theta =1\\ \Rightarrow \theta =\frac{\pi }{4},\frac{3\pi }{4}\\ r>0,0\le \theta <2\pi \end{array}$