Why do we measure angles in terms of fractions of pi? Because trigonometric functions are defined in terms of pi. So why are trigonometric functions defined in terms of pi? Because angles are defined in terms of pi. Pi isn’t even a rational number. Not only is it irrational, it’s trancedental which means it can’t be expressed as the root of a polynomial.You’d would be hard pressed to find a unit lessorderly to base angles off of.

Angles should be measured in terms of 1. That way 45 degrees or whatever radians are 1/4 which makes more sense because it’s a quarter turn.