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.