## BLOG-93

1) Directed Angles:

The initial arm rotates through certain amount of rotation in clockwise or anti-clockwise direction to the terminal arm then this amount of rotation is called as the measure of directed angle and such an angle is called as directed angle.

The directed angle AOB has ray OA as an initial arm and ray OB as the terminal arm. O is called as vertex of an angle AOB.
Note:
1) Here, Angle AOB ≠ Angle BOA even if they have same amount of rotation.
2) If the rotation of initial arm is anticlockwise, the directed angle is positive and if it is clockwise then the angle is negative.

See the figure carefully to understand the concept.

2) The Zero Angles:

The amount of rotation of ray OA about O is zero then the directed angle is called zero angle. (Here initial arm OA and the terminal arm OB coincide).

3) The Straight Angles:
If an initial ray OA and the terminal ray OB are opposite rays then the directed angle is called Straight angle

4) Degree measure:

Here an angle is measured in degree.
(1/360)th  part of a complete rotation is called as one degree and is denoted by 10
(1/60)th  part of a complete rotation is called as one minute and if denoted by 1'
(1/60)th  part of a complete rotation is called as one second and if denoted by 1"

Here an angle is measured in radian.

Let r be the radius of a circle with center O. A and B are any two points on the circle with arc length equal to radius r. Then the measure of the central angle AOB is of measure 1 radian and is denoted by 1c.

6) Relation between radian measure and degree measure:
1= (π/180)= 0.01745 c approximately.
1= (180/π) 0 = 57.2958280
1= (180/π) 0 = 5717' 48"