2006-09-24 04:53:53 · 9 answers · asked by Ajay I 1 in Science & Mathematics ➔ Mathematics
Because radians more directly relate to the properties of the circle. Later, many formulas are *much* easier when done in radians rather than degrees.
2006-09-24 05:00:40 · answer #1 · answered by mathematician 7 · 0⤊ 0⤋
Think this way, why is a circle 360 degrees? Why not 100 degrees?
Radian system is a logical system that resolves many complicated problems, it does not make life difficult.
Like, to calculate length of an arc, in degree system you use the formula l= Ó¨/360 * 2*pi*r
Now 2*pi/360 is a constant. What if we donot have to consider all these constants all the time?
That is possible if we multiply Ó¨ by 2*pi/360. So the radian system was introduced where all degree angles are multiplied by 2*pi/360.
Angle in radian Ǿ = (2*pi/360) * Ө
Length of an arc is simply Ǿ * r.
Ǿ = length of arc / radius.
So in a circle, length of arc = circumference = 2*pi*r
So Ǿ = 2*pi*r/r = 2*pi.
Now that is quite logical. Moreover, It is easier to calculate.
2006-09-24 20:20:32 · answer #2 · answered by astrokid 4 · 0⤊ 0⤋
An angle is a measurable value whereas a radian is a constant or derived value. In mathematics it can be termed as a proportioality constant. For example, the circumfrence of a circle is directly proportional to the radius of it. To remove the proportionality , a constant has to be introduced . If the constant is practically found as one, the equation becomes C=D. In our case it is not so. It needs a constant figure 3.14285... to match with the actual measured value of the circumfrence. In a circle one Pi=180 degree. Pi=22/7 or 3.14285....So Pi=D/C where D is the diameter of the circle and C is the circumfrence of the circle.
But 180 degree angle can not be substituted in this equation against Pi. So we can not say radians as a measured value. So the equivalent of measured value of degree is only used for calculation purpose. One degree is equivalent to 0.01746...radians.
2006-09-24 10:18:13 · answer #3 · answered by ramchand_l 1 · 0⤊ 0⤋
In many existing formula degrees can not be used or for that matter new formulas may require the use of radians also.
Some times radian is easy to use and at other time degrees.
2006-09-24 09:21:30 · answer #4 · answered by minootoo 7 · 0⤊ 0⤋
Because radians include pi which relate it to the circle
Plus, degrees is technically not a mathematical concept.
Radians is mathematically derived, and therefore more convenient.
2006-09-24 05:12:14 · answer #5 · answered by Anand 2 · 0⤊ 0⤋
coz radian is based on pi(22/7approx)a
imp mathametical constant
2006-09-24 05:02:12 · answer #6 · answered by soumyaxyz 2 · 0⤊ 0⤋
Radians are units of S.I. system.......
2006-09-24 06:58:02 · answer #7 · answered by hotshot 2 · 0⤊ 0⤋
coz they have just got 2 complicate the things more for students!!!!!
2006-09-24 05:05:37 · answer #8 · answered by manasi p 2 · 0⤊ 0⤋
because pi (3.14159...) is very much still in use everywhere, and that pi is in radians
2006-09-24 04:55:09 · answer #9 · answered by sebourban 4 · 0⤊ 2⤋