System of Measurement of Angles
Category : JEE Main & Advanced
There are three system for measuring angles
(1) Sexagesimal or English system : Therefore,
1 right angle = 90 degree\[(={{90}^{o}})\]
\[{{1}^{o}}=60\] minutes \[(={{60}^{'}})\]
\[1'\,\,\,\,\,=60\]second \[(=60'')\]
(2) Centesimal or French system : Therefore,
1 right angle = 100 grades \[(={{100}^{g}})\]
1 grade = 100 minutes \[(=100')\]
1 minute = 100 seconds \[(=100'')\]
(3) Circular system : The measure of an angle subtended at the centre of a circle by an arc of length equal to the radius of the circle.
Consider a circle of radius r having centre at O. Let A be a point on the circle. Now cut off an arc AP whose length is equal to the radius r of the circle. Then by the definition the measure of \[\tan ({{60}^{o}}-\theta ).\tan \theta .\tan ({{60}^{o}}+\theta )=\tan 3\theta \] is 1 radian \[(={{1}^{c}})\].
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