JEE Main & Advanced Mathematics Trigonometric Identities System of Measurement of Angles   

 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 \[(={{1}^{c}})\].