Page 28 - Mathematics Class - XI

OBSERVATION
1. Using thread or yarn, measure arc lengths of the circle CA, AD, CB and BD respectively as shown in
figure (c) and record them in the table given below.

S. No. Name of arc Length of arc (l) Radius of circle (r) Radian measure


1 CA ∠COA = CA =

r

2  ∠AOD =  =
AD
AD
r

3 CB ∠COB = CB =

r

4 BD ∠BOD = BD =

r

2. With the help of protractor, measure the angles in degrees and complete the table given below.

Degree measure
Angle Degree measure Radian measure Ratio =
Radian measure
∠COA

∠AOD

∠COB

∠BOD

CONCLUSION
This activity verifies the relation between the degree measure and the radian measure of an angle.
i.e., 1 radian = 57.29°

APPLICATION

This result is used for the study of trigonometric functions.

Knowledge Booster

● Degrees are easier to use in everyday work, but radians are much better for mathematics.
● The relation between degree measure and radian measure of some common angles are given in the following table:
Degree 30° 45° 60° 90° 180° 270° 360°
p p p p 3p
Radian p 2p
6 4 3 2 2

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