Lines- Common Polar Coordinate Graphs
A few lines have quite simple equations in polar coordinates.
1. θ = β
We are able to see that this is a line by converting to Cartesian coordinates as follows
θ = β
tan-1 (y/x) = β
y/x = tan β
y = (tan β) x
This is a line that undergoes the origin and makes an angle of β along with the positive x-axis. Or, in other words it is a line by the origin with slope of tan β.
2. r cos θ = a
This is very easy to convert to Cartesian coordinates to x = a. Thus, this is a vertical line.
3. r sin θ = b
Likewise, this converts to y = b and so is a horizontal line.