We know that circumference of a circle of radius is , and angle formed by one complete revolution is radian, therefore,

Thus we have the relationship

Further

** Example**:

Convert the following angles in degree:

(i) radians

(ii)

** Solution**:

(i)

(ii)

** Example**:

Convert into radians.

** Solution**:

Most calculators automatically would convert degree into radians and radians into degrees.

** Example**:

An arc subtends an angle of at the center of a circle and its length is . Find the radius of the circle.

** Solution**:

and

** Example**:

Find the length of the equatorial arc subtending an angle of at the center of the earth, taking the radius of the earth as 5400km.

** Solution**:

and

Now