Since the roots have to add up to zero, this means that: ... Since the trisection equation has no constructible roots, and since cos(20°) is a root of the trisection equation, it follows that cos(20°) is not a constructible number, so trisecting a 60° angle by compass and straightedge is impossible.

Is it possible to Trisect an angle?

Angle trisection is a classical problem of straightedge and compass construction of ancient Greek mathematics. ... It is possible to trisect an arbitrary angle by using tools other than straightedge and compass.

What happens when you Trisect an angle?

Angle trisection is the division of an arbitrary angle into three equal angles. It was one of the three geometric problems of antiquity for which solutions using only compass and straightedge were sought.