**
** ** (III) The Circular system (or the Circular
measure) : **This system is commonly used in all the higher branches
of mathematics.
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**
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 360^{0}Then 2p (rad) = 360^{0}
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**
**Theorem :**
A radian is independent of the radius of the measuring
circle.
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** **
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**EXAMPLE 2**
Convert 60 13' 18 to degrees in decimal notation.
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**Solution :**
**
**We know 1' = (1/60)^{0 } and 1" = (1 / 60)' **
**
**EXAMPLE
3 **
Convert 87.41290 to degrees, minutes and seconds.
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**
**Solution : **
Firstly 0.41290 = 0.4129 (60') = 24.774'
Also, 0.774' = 0.774 (60") = 46.44"
Thus 87.4129^{0} = 870^{ } 24' 46.44"
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**EXAMPLE 4 **
Convert 1 rad into degrees, minutes and seconds.
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**Solution :**
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**EXAMPLE 5 **
Convert 1 degrees to radians
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**Solution :**
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