Hi Paula,

The practically of using radian measure is that many of the mathematical expressions involving angle measurement are simpler when using radian measure than when using degrees. Specificaly the derivatives of trig functions are much easier to express if the angles are measured in radians rather than degrees. If you are dealing with the rate of change of an angle then you are probably going to need the derivative and hence there is an advantage to using radians.

Dealing with the rate of change of an angle is much more common than you might think. In North America the electricity delivered is to our houses at 60 Hz (60 hertz where one hertz is one cycle per second), middle c is 261.625565 hertz, the tachometer in my car registers in revolutions per minute, the processor in my computer runs at 2.66 GHz. These are all in revolutions or cycles per unit time but the people who work with these quantities more often use the units radians per unit time. One revolution or cycle is 2π radians and when using cycles or revolutoions the factor 2π appears quite often and complicates the expressions and introduces additional round off error in the calculations.

What professionals might use radians? Any engineer or scientist who deals with electricity, someone who works with electronic music, automotive engineers, electronic circuit designers, and my favourite, mathematicians.

I hope this helps,
Harley