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Angle Measure — (Degrees and Radians)

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


Angle of any magnitude can be created by this concept.



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

Remember:- 1 revolution = 360°

                   1° = 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

(is in radians)

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

see diagram below

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

Formula for conversion
Radian ------------ Degree

Degree ---------→ Radian

Example 1: Convert (-47°30' )to radians

Example 2:
Convert radians to degrees

Example 3:
In a circle of diameter 30cm, there is a chord of length 15cm. What is the length of the minor arc cut off by the chord?

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