Measurement of angles

Degrees. There is a common system for the measurement of angles. The degree is the unit of measurement.

The angle of one degree 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 60 equal parts called seconds. The symbols °, ' , " are used to denote degrees, minutes and seconds respectively. Thus angle of 31 degrees 15 minutes and 10 seconds may be written 31° 1540".

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 being placed with its vertex at the centre of any circle subtends on circumference an arc equal in length to the radius of the circle. We may say that the length of an arc of a circles equal to the radius of the circle multi plied by the measure in radians of the angle subtended by the arc at the centre of the circle. To convert degrees to radians, divide the number of degrees by 180/&П7 or multiply by /180. To convert radians to degrees, multiply the number of radians by 180/bf.

Exercises:

1. Make up sentences of your own using the words and expressions given below:

in one degree, the unit of measurement, convert, to express an angle, in the system, equal in length to, subtended by.

2. Answer the following questions:

1. What units of measurement of angles do you know?

2. What is called a degree?

3. Into how many parts is the degree divided?

4. How do we measure angles by using the radian?

5. How can degree be converted into radians?

3. Give English equivalents of the following:

общая система измерения углов, 1/360 часть полного оборота, делится на 60 равных частей, единица измерения, длина дуги окружности, чтобы перевести радианы в градусы, умножить число радиан,

4. Read the text. Ask 5 questions to it:

Angles Measured in Degrees

Just as in the case of length, it is often convenient to employ a smaller unit than the meter or yard; so also, in angular measurement, a smaller unit than the right angle is generally used. This unit is the one-ninetieth part of the right angle; it is called a degree and is denoted thus: 1.

Two angles whose sum is a right angle are called complementary angles, and each is called the complement of the other.

Thus angles of 30 and 60 are complimentary, because 30+60 = 90, or a right angle.

Two angles whose sum is two right angles are called supplementary angles, and each is called the supplement of the other.

5. Translate into Russian:

Circumference of any circle is divided into 360 equal parts and lines are drawn from the centre of the circle through each point of division. For measuring very small angles the degree is divided into 60 equal parts each of which is called one second of an angle. There are thus 21600 minutes in a circle, 3600 seconds in one degree, and 1296000 seconds in a circle.