The Maclaurin trisectrix is a curve first studied by Colin Maclaurin in 1742. It was studied to provide a solution to one of the geometric
problems of antiquity, in particular angle trisection,
whence the name trisectrix. The Maclaurin trisectrix is an anallagmatic
curve, and the origin is a crunode.

The asymptote has equation , and the center of the loop is at . If is a point on the loop so that the line makes an angle of with the negative y-axis,
then the line
will make an angle of with the negative y-axis.