you already know that 360 deg converts to 2*pi rad.now if you wanted to convert alpha deg to rad,then you can use proportion. 360 to 2*pi is like alpha to beta where beta is alpha converted to rad.
so you get 360: (2*pi)=alpha:beta.
cross multiply to get 360 deg*beta=2*pi*alpha
dividing by 360deg you get: beta=(pi*alpha)/180deg
this is the actual formula for the conversion,so if you put in 30 deg for alpha you will get pi/6.nothin missin,everythin in its place.