Circular radius of length theta:
Where r is the radius of the circle l, is the length of the arc and theta mathematical denoted by θ is the circular measure of the central angle.
By definition of radian:
An angle of 1 radian extend an arc AB on the circle of length = 1.r
An angle 1/2 radian extend an arc AB on the circle of length = 1/2.r
An angle of 2 radians extend an arc AB on the circle of length= 2.r
Therefore,
An angle of θ radian extend an arc AB on the circle of length = θ. r
implies that means (⇒)
⇒ l = θ.r
Therefore, The Formula of theta in radian.
θ= l / r
Definition of radian and unit radian:
Radian is the measure of the angle expanded at the center of the circle by an arc (mean curve), whose length is equal to the radius of the circle.
UNIT RADIAN:
Consider a circle of radius r, make an angle ∠ AOB at the center of the circle whose rays cut off an
arc ⌢ AB
on the circle whose length is equal to the radius.
Thus
m ∠ AOB= 1 radian