ANGLES AND ITS DIFFERENT UNITS

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Positive angleAngle is a measure of rotation of a given ray about its initial point. 

Negative angle
The original ray is called the initial side and the final position of the ray after rotation is called the terminal side of the angle.

  • The point of rotation is called the vertex.
  • If the direction of rotation is anticlock, the angle is said to be positive.
  • If the direction of rotation is clock, then the angle is negative.
The measure of an angle is the amount of rotation performed to get the terminal side from the initial side.

There are several units for measuring angles.

Degree measure
  • If a rotation from the initial side to terminal side is ( 1/360 )th of a revolution, the angle is said to have a measure of one degree ( 1° ).
  • A degree is divided into 60 minutes ( 60' ).
  • A minute is divided into 60 seconds ( 60" ).
One sixtieth of a degree is called a minute, i.e. 1', and one sixtieth of a minute is called a second, i.e. 1".
Thus,     1° = 60' ,  1' = 60"


Radian measure
  • Another unit of measurement of an angle, called the radian measure.
  • Angle subtended at the centre by an arc of length 1 unit in a unit circle is said to have a measure of 1 radian.
In a circle of radius r, an arc of length r subtend an angle of 1 radian.

An arc of length l subtend an angle measure is l/r radian. 

Thus, if in a circle of radius r, an arc of length l subtend an angle ϴ radian at the centre. 

ϴ = l/r  or l = rϴ

Relation in degree and radian 

Relation in degree and radian

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