The first question on the first chapter of E. W. Hobson's A Treatise on Plane Trigonometry asks:
What must be the unit of measurement, that the numerical measure of an angle may be equal to the difference between its numerical measures as expressed in degrees and in circular measure?
Given that the only other angle measure introduced before the question is the grade (1/100 of a right angle), how can one solve this without resorting to negative angles?
In this system the numerical measure of a right angle is (90- π/2) So that (90-π/2) units is a right angle Therefore unit= 1/(90-π/2) × right angle