Radian angle in Trigonometry

[shahar]

Why is Radian angle representation more convenient than the degree representation in Trigonometry?
Which are the cases when we can use the degree representation for angles than the Radian representation?

 

[LCKurtz]

The answer lies in calculus. The radian is the natural unit of measurement because only for that does the derivative of [MATH]\sin x[/MATH] equal [MATH]\cos x[/MATH]. That makes many formulas and calculations easier. But it is true that any calculation done in radians can be done in degrees.

 

[Deleted member 4993]

Why is Radian angle representation more convenient than the degree representation in Trigonometry?
Which are the cases when we can use the degree representation for angles than the Radian representation?

It is also a matter of convenience. It is more convenient to divide a circle into 8 sections (45^o) - than into \(\displaystyle \frac{\pi}{4} \ \)sections.

 

[yoscar04]

An additional point is that radians has no dimensions (i.e. meter), which is necessary in order to be able to write trigonometric functions as Taylor expansions.

 

[HallsofIvy]

First, the "radian" is a more natural unit than the "degree". To define "degrees" we arbitrarily divide the entire circle into 360 parts. To define degrees, we take the ratio of an arc (part of a circle) of radius r to the corresponding part of a circle of radius 1.

Because of that, as yoscar04 said, a "radian" isn't really a "unit" like a "degree" is. It is a ratio of two measurements with the same unit and "meter/meter" is unitless.