If a rotation from the initial side to terminal side is of a revolution, the angle is said to have a measure of one degree, written as
.
A degree is divided in 60 minutes and a minute is divided in 60 seconds
Some angles are shown below (In degree)
Radian Measure
Angle subtended at the centre by an arc of length in a unit cirlce (circle of radius
is said to be a measure of
radian.
The circumference of a circle of radius . Thus, one complete revolution of the initial sides subtends an angle of
radian.
In a circle of radius , an arc of length or subtends an angle whose measure is
radian, an arc of length
will subtend an angle whose measure is
.
Thus, is a circle of radius , an arc length length
subtends an angle
radian at centre, we have
Some angles whose measures are in radian shown below:
Relation Between Degree and Radians
Or
Also,
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Radian | ![]() |
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Notational Convention
Example:
Convert into radian.
We know
Example:
Find the radius of the circle in which a central angle of intercepts an arc of length
Solution:
Here,
Hence,
Example:
Convert radian in degree measure
Solution:
We know