What is the significance of measuting angles in radians. though it is so inconvinient?

Question

For example measuring angluar velocity

Answer 1

Actually, radians are *more* convenient. Many formulas are much easier with radians than with degrees. For example, the area of an angular sector of a circle has a much simpler description in radians than in degrees. The point is that radians are more closely associated with the actual geometry of the circle than degrees are. Later, when you do calculus of trig functions, radian formulas are *much* easier.

Answer 2

Radians are just yet another unit of measure, like degrees. 2 X pi radians is mathematically equivalent (~) to 360 deg. So pi radians ~ 180 deg, pi/2 radians ~ 90 deg, and so on. Often we simply write "pi/2," for example, and leave the word "radians" off.

Sometimes radians are easier to use than degrees. For example, check this out:

"The radian is useful to distinguish between quantities of different nature but the same dimension. For example, angular velocity can be measured in radians per second (rad/s). Retaining the word radian emphasizes that angular velocity is equal to 2π times the rotational frequency. " [See source.]

As a physics grad, one of the most frustrating issues about physics was having to learn multiple equations and constants because of the different units of measure. Unfortunately, I don't see that issue disappearing soon.