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

                       
                 
                   radian

            Thus we have the relationship
                         radian       =  
                   radian          =  
                  1 radian            =  
            Further                    =   radian
                                                =   radian

Example:
            Convert the following angles in degree:

                        (i)  radians                         (ii) 3 radians

Solution:          (i)  radians  =
                                                  =

                        (ii) 3 radians     = 3 (1 radian)
                                                = 3

Example:
            Convert  into radians.

Solution:                   =  
                                                =  
                                                =   radians
                                                =   radians.
            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:           radians rad  radians.
                     radian            and      
                                

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

Solution:
                               radian 
                                  and       km
            Now           
                                           km.