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(III) The Circular system (or the Circular
measure) : This system is commonly used in all the higher branches
of mathematics.
The only unit of this system is a radian (c)
* A radian (rad) is defined as the measure
of an angle subtended by an arc of a circle
equal to the radius of the circle. The circumference
of a circle = 2 pr and subtends an angle
of 3600Then 2p (rad) = 3600
 
Theorem :
A radian is independent of the radius of the measuring
circle.
EXAMPLE 2
Convert 60 13' 18 to degrees in decimal notation.
Solution :
We know 1' = (1/60)0 and 1" = (1 / 60)'
EXAMPLE
3
Convert 87.41290 to degrees, minutes and seconds.
Solution :
Firstly 0.41290 = 0.4129 (60') = 24.774'
Also, 0.774' = 0.774 (60") = 46.44"
Thus 87.41290 = 870 24' 46.44"
EXAMPLE 4
Convert 1 rad into degrees, minutes and seconds.
Solution :
EXAMPLE 5
Convert 1 degrees to radians
Solution :
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