The Trisectrix as the Locus of Points of Intersection
A trisectrix (red) is the locus of the points of intersection (red point ) of a moving horizontal line (blue) and a rotating line (black).[more]
Initially, the line lies along the line and the line lies along the line . The line rotates clockwise about the origin at 1 radian per time unit, and the line moves toward the axis at a constant rate of units per time unit, so that both lines reach the axis at the same time. The line meets the axis at an angle .[less]
The trisectrix can be used to trisect an angle. If a vertical line is dropped from to meet the axis at , the point on the line is such that , and the horizontal line meets the trisectrix at , then the angle that makes with the axis is .
 T. Heard, D. Martin, and B. Murphy, A2 Further Pure Mathematics, 3rd ed., London: Hodder Education 2005 p. 202, question no. 2.