Trigonometry
Trigonometric Functions
Unit of measurement of angles - a radian (the circular measure)
Protractor - an instrument for measuring angles
Unit of measurement of angles - a radian (the circular measure)
The relation between a central angle a (the angle between two radii) and the corresponding arc l in the circle of radius r is shown by the proportion,
 a° : 360° = l : 2rp It shows that the central angle a° compared to the round angle of 360° (called perigon) is in the same relation as the corresponding arc l compared to the circumference 2rp. Therefore,

 where the ratio we call the circular measure, usually denoted arad, i.e.,
 thus,
The central angle subtended by the arc equal in length to the radius, i.e. l = r,
 we call it radian. Thus, the angle a = 1° equals in radians,

or arc1° = 0.01745329. Arc is abbreviation from Latin arcus, (p = 3.1415926535...).
Protractor - an instrument for measuring angles
Mentioned relations between units of measurement of an angle and arc clearly shows the protractor shown in the below figure marked with radial lines indicating degrees, radians and rarely used gradians (the angle of an entire circle or round angle is 400 gradians).
The hundredth part of a right angle is 1g grad, and one 100th part of 1grad is centesimal arc minute 1c, and one 100th part of centesimal arc minute is centesimal arc second 1cc, therefore