# Angle Measure â€” (Degrees and Radians)

To create angles greater than 90Â° and find trigonometric ratios of these angles, we use the idea of rotation

Angle of any magnitude can be created by this concept.

Examples:

Degree measure:- of a revolution is called 1Â°. A degree is divided into 60 minutes and a minute is divided into 60 seconds.

Remember:- 1 revolution = 360Â°

1Â° = 60 minutes (60')
1' = 60 seconds (60")

Radian Measure:- This is another unit in which angles are measured. In higher classes we use radian measure instead of degrees. When your learn calculus, you will realize that many results are true only for radians and not for degrees.

[in limits, differentiation, integration etc.]

Definition:- Radian is the angle subtended at the centre of a circle of radius
r units by an arc whose length is also r units. 1 radian is written as 1c or simply 1.

In a circle of radius r units, arc of length l subtends an angle

Since the circle has circumference (perimeter) 2Ï€ r units, there can be 2Ï€ arcs of length r units along the circumference. Hence the total angle at the centre is 2Ï€ c

see diagram below

Table - I Conversion from degrees to radians.
 Degree 0 30Â° 45Â° 60Â° 90Â° 180Â° 270Â° 360Â° 720Â° Radian 0

Formula for conversion