Question

Choosing a Convenient Coordinate System Compare the rectangular equation of the line$r=2$ with its polar equation. In which coordinate system is the equation simpler? Which coordinate system would you choose to study lines?

Short answer

The given equation of a line$y=2$ is.$r\sin \theta =2$ The simpler equation is in rectangular coordinates.

Step-by-step solution

Step 1. Given information

An equation of a line in rectangular coordinates,$y=2$

Step 2. Concept used

To convert polar coordinates into rectangular coordinates use formulas-

$x=r\cos \theta \&y=r\sin \theta$

To convert rectangular coordinates into polar coordinates use formulas-

$\begin{array}{l}r=\sqrt{x^2+y^2}\\ \tan \theta =\frac{y}{x}\end{array}$

Step 3. Calculation

The given equation of the line is,$y=2$

changing into the polar form we get$r\sin \theta =2$.. Comparing it with the rectangular equation we can see that the given equation in rectangular coordinates is simpler.