# Conversion of Radians into Degrees and Vice Versa

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

Thus we have the relationship

Further

** Example**:

Convert the following angles into degrees:

(i) radians

(ii)

** Solution**:

(i)

(ii)

** Example**:

Convert into radians.

** Solution**:

Most calculators automatically would convert degrees 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