Relation Between Three Systems of Measurement of an Angle
Category : JEE Main & Advanced
Let D be the number of degrees, R be the number of radians and G be the number of grades in an angle \[\theta ,\] then \[\frac{D}{90}=\frac{G}{100}=\frac{2R}{\pi }\]
This is the required relation between the three systems of measurement of an angle.
Therefore, one radian \[\cos A.\cos 2A.\cos {{2}^{2}}A.\cos {{2}^{3}}A.......\cos {{2}^{n-1}}A=\frac{\sin {{2}^{n}}A}{{{2}^{n}}\sin A},\,\text{if }A=n\pi \]radians \[={{180}^{o}}\]
i.e., 1 radian \[=57{}^\circ 1{7}'44.{{8}'}'\approx {{57}^{o}}1{7}'4{{5}'}'\].
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