Measures of Angles

There are three standard systems of measuring angles, namely, the revolution system, the degree system and the radian system.

A simple but logical system is the revolution system. In this system, an angle is measured by the number of revolution or fraction of a revolution made by the terminal side in relation to the initial side. The unit of measurement in this system is revolution (rev) which is equivalent to one whole angle.

The second system of measuring angle is the degree system. It is patterned after the sexagesimal system of ancient Babylon. In this system the units of measurement is in degree (°). A degree is an angle formed by a rotation about its vertex equal to 1/360 of a complete revolution. The whole angle is divided into 360 degrees or 360° a number that is multiple of 60.

The degree is further divided into minutes ( ' ) and minutes into seconds ( " ) with the following conversions:

1° = 60' (min.)
1' (min.)= 60" (sec.)

1° = 3600" (sec.)

The third system of measuring angle is based on the relation between the radius an the circumference of a circle. This is known as the radian system wherein the unit of measurement is the radian (rad). An angle of one radian is a central angle describe by an arc whose length is equal to the radius of the circle.








CONVERSION TABLE:

RADIAN TO REVOLUTION


1rad = 1/2π rev.

2π = 1rev.

RADIAN TO DEGREE


π rad = 180°


DEGREE TO REVOLUTION


1° = 1/360 revolution