Measurement of angles

Degrees. There are common system for the measurement of angles. In one the degree is the unit of measurement.

The angle of one degree is the angle which requires 1/360 of the rotation needed to obtain one complete revolution.

Thus a complete revolution is divided into 360 equal parts called degrees. Each degree is divided into 60 equal parts called minutes, and each minute — into sixty equal parts called seconds. The symbols º,', " are used to denote degrees,

minutes and seconds respectively. Thus angle of 31 degrees, 15 minutes and 10 seconds may be written 31°15'10".

Radians. In the second system used for measurement of angles, the radian is the unit of measure.

A radian is the measure of an angle which, placed with its vertex at the centre of any circle, subtends on the circum­ference an arc equal in length to the radius of the circle. Thus if we take a circle with centre at 0 and radius r and from a point A on the circum­ference measure an arc AB of length r, the angle AOB is by defi­nition an angle of 1 radian (Fig. 31). We may say that the length of an arc of a circle is equal to the radius of the circle multiplied by the meas­ure in radians of the angle subtend­ed by the arc at the centre of thecircle. To convert degrees to radi­ans, divide the number of degrees by 180/π, or multiply by π/180 to convert radians to degrees, multiply the number of radians by 180/π.