Why all select radian measure more than degree measure?

Answer 1

The relationship between the radius and circumference of a circle and related shapes becomes simpler.

Trigonometric ratios can be defined as infinite series more simply in terms of radians:

for example: sin(x) = x - x3/3! + x5/5! - ...

And last, my favourite equation:

e(i*pi) + 1 = 0 (Euler's equation)

would not have the same beauty and brevity.