Question No.  19863 :
How is radian useful in our daily lives? Why can't degree always be used? Is there some advantages of using radian over degree?

The radian is the SI derived unit of angle. It is defined as the angle subtended at the centre of a circle by an arc of circumference equal in length to the radius of the circle. Thus the radian measure (or circular measure) of an angle is the ratio of the arc it subtends to the radius of the circle in which it is the central angle (a constant ratio for all such circles). Hence the angle of an entire circle is 2(about 6.283185) radians. One radian is approximately 57 degrees, and 1 degree is /180 or approximately 0.0175 radians. The radian represents essentially a sector of the circle, marking off 57.29577951 degrees of a 360-degree circle. The number 360 has been historically established and conventionally accepted as representing the number of theoretical sectors/degrees within a circle. Our time measures (1 h = 60 min, 1 min = 60 s), as well as the division of the full angle into 360 degrees recall the sexagesimal system (base 60) of the Babylonians. Obviously, a circle may have as many sectors/degrees as one might wish to physically divide the circle into for computational reasons. Sexagesimal measure of an angle refers to the system in which one complete revolution is divided into 360 parts, called degrees; one degree into 60 parts, called minutes; and one minute into 60 parts, called seconds. In the centesimal system of measuring angles, one-hundredth part of a right-angle is called a grad (or grade). Radians are commonly used to specify angles in polar co-ordinates. In mathematics, angles must be represented in radians in trigonometric functions, to make identities and results as simple and natural as possible. For example, there are formulae of infinite series such as: sin x = x - x3/3! + x5/5! - x7/7! + x9/9! - x11/11! + ˇˇˇˇˇ cos x = 1 - x2/2! + x4/4! - x6/6! + x8/8! - x10/10! + ˇˇˇˇˇ where x is expressed in radians. These simple and natural formulae would not be valid if x were expressed in degrees. The radian was formerly an SI supplementary unit (symbol rad), but this category was abolished from the SI system in 1995. The definitions of the supplementary units - radian and steradian - are gratuitous. These definitions properly belong in the province of mathematics and there is no need to include them in a system of physical units. Question Asked By:

Name: Yipei

Age Group: 13 to 20

Occupation Type: Student

Education Level: N/O Level's