Q. Define Radian.

Answer:

Radian:

The most natural way to measure the angle θ is not a degree but a radian. It is a two-dimensional plane angle and it is defined as, " the angle (θ) subtended at the center of the circle by an arc with a length equal to the radius of that circle", as shown in the figure and it is equal to the ratio between the lengths of the arc and radius. It is denoted by 'rad'.



Let the angle  "θ", which is subtended by an arc of length "S" along a circle of radius "r" then;

θ = `\ frac {S}{r}`(rad) -------(1)

  For one revolution.

Length of the boundary of the circle (S) = circumference of the circle = 2πr


by putting values { S = 2πr } in equation (1)

θ = `\frac {2πr}{r}` = 2π rad

This shows that 

Numbers of radians in One revolution = 2π rad 

= 2ｘ 3.1416 rad 

= 6.2832 rad

There are a little more than 6 radians in one full rotation.


⇒ From equation (1) 

S = r θ ---------------(2)


Again using equation (1) when the length of the arc is equal to the length of the radius of that circle i.e. S = r

θ = `\frac {r}{r}` = 1 rad  (shown the figure above)


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