Plane Trigonometry

Angular Measurement

600 The unit of Circular measure is a Radian, and is the angle at the centre of a circle which subtends an arc equal to the radius. Hence 601 Circular measure of an angle=arcradius. 602 Circular measure of two right angles=3.14159⋯≡𝜋. 603 The unit of Centesimal measure is a Grade, and is the one-hundredth part of a right angle. 604 The unit of Sexagesimal measure is a Degree, and is the one-ninetieth part of a right angle. 605 To change degrees into grades, or circular measure, or vice versa, employ one of the three equations included in 𝐷90=𝐺100=2𝑅𝜋 where 𝐷, 𝐺, 𝐶 are respectively the numbers of degrees, grades, and radians in the angle considered.

Sources and References

https://archive.org/details/synopsis-of-elementary-results-in-pure-and-applied-mathematics-pdfdrive