Q. Derive a Relation between degrees and radians

Answer:


For one complete rotation, there are 360°

Degrees in one revolution = 360° ---------(1)

and 

Numbers of radians in 1 revolution = Circumference of the circle ➗ Radius of that circle

Numbers of radians in 1 revolution = `\frac {2πr}{r}`

Numbers of radians in 1 revolution = 2π rad --------(2)


We know that number of degrees in one revolution is equal to the number of radians in one revolution, so

2π rad = 360°



1 rad = `\frac {360°}{2π}`

1 rad = `\frac {360°}{2ｘ 3.1416}`

1 rad = 57.3° the required relation between radians and degrees


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