trisectent

Trisectent is a term used in trigonometry and geometry. It refers to a specific angle measurement or a geometrical concept related to dividing an angle into three equal parts. In trigonometry, it might be used in the context of trigonometric functions of angles that are one-third of another angle. For example, the triple angle formula relates the sine or cosine of an angle to the sine or cosine of three times that angle. The trisectent would then be the angle that, when multiplied by three, yields the angle in question.

Geometrically, the problem of trisecting an arbitrary angle using only a compass and straightedge is a classical construction problem. It has been proven that such a trisection is impossible for all angles. While some specific angles, like 90 degrees, can be trisected (yielding 30 degrees), a general method that works for any angle cannot be achieved with these tools alone. This impossibility is a significant result in classical geometry. The term "trisectent" therefore can also imply the angle resulting from such a division, even if the division itself is not generally constructible.