Question

Rectangular Equations to Polar Equations

Convert the equation to polar form. $y=5$

Short answer

The polar equation is $r=5\mathrm{cosec}\theta$

Step-by-step solution

Step 1. Given information

An equation is given in a rectangular coordinate system as$y=5$

Step 2. Concept used

Substitute values in the equations, do computations and simplify the problem. For a precise response, consider a given range or radius and angle. There exist an endless number of equations if this is not the case.

Step 3. Calculation

Formulae used,

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

Substitute the values in the formulae,

$\begin{array}{l}\Rightarrow y=5\\ \Rightarrow r\sin \theta =5\\ \Rightarrow r=5\mathrm{cosec}\theta \end{array}$