2006-08-05 07:01:18 · 10 answers · asked by mortangle2006 2 in Science & Mathematics ➔ Mathematics
degrees are baesd on nothing except somebody decided 360 = one turn. radians are dimensionless and are based on the fundamental geometry of circles (arc length / radius). Anything involving radians can use degrees except they must be converted. degrees can't be squared, multiplied, etc. radians can.
For example, centripetal acceleration = r *w^2 where r is radius and w is angular speed in radians per second. if in radians per second, no units problems answer is distance per sec^2 (radians is dimensionless length /length. if w is in degrees, you get distance / (degrees^2 * seconds^2) which has no physical meaning.
2006-08-05 07:10:13 · answer #1 · answered by Anonymous · 0⤊ 1⤋
First, degrees are based on the Babylonian base-60 system which assigns 360 degrees to a circle. That's artificial, of course. Radians are based on the relationship that pi times the radius equals the circumference of a circle, regardless of what number system you use. So radian measure is natural, nolt artificial.
Second, when you plot the trig functions, radian measure works better. pi/2 is 90 degrees; 2 pi radians equals a full circle, 360 degrees.
Also (but I forgot the formula), there's a relationship, maybe involving a calculus integration or an infinite series, that relates pi and e, the base of the natural log system. I think it's called Euler's Formula, and I think radians are part of that.
Not sure about this last, however. It's just something in the back of my head.
2006-08-05 07:20:43 · answer #2 · answered by bpiguy 7 · 0⤊ 0⤋
Most importantly, radians are compatible with the measure of the real line:
By definition, 1 radian is the angle such that the length of the arc from the point on the unit circle that subtends the x-axis to (1,0) is 1 unit.
In mathematics courses from calculus to beyond, you will almost exclusively work in radians.
Be sure to memorize your unit circle and the principal values! It will pay off when you take calculus :)
2006-08-05 07:24:02 · answer #3 · answered by Anonymous · 0⤊ 0⤋
In actuality, radians are a more precise measurement than degrees. This is because the nature of radians is based on the ratio defined by pi.
In various mathematical applications, radians create easier conversions. Calculus, for example, works easier with radians than degree measure.
2006-08-05 07:12:49 · answer #4 · answered by Jim T 6 · 0⤊ 0⤋
You're right: radians are just another measure of angle, and there is no special one. However, radians are a natural measurement (whereas degrees are completely arbitrary) because they relate angle to arc length around a circle with its center on the vertex. If you were just handed such a figure with no ruler around, you might try to define everything in terms of the radius of the given circle--which is what radians do.
2006-08-05 07:13:19 · answer #5 · answered by Benjamin N 4 · 0⤊ 0⤋
radian is better to operate for example trignometic expansion in terms of radian
2006-08-05 12:40:03 · answer #6 · answered by Mein Hoon Na 7 · 0⤊ 0⤋
Click on the URL below for additional information
www.mathforum.com/library/drmath/view/64034.html
www.gamedev.net/community/forums/topic.asp?topic_id=301680
2006-08-05 08:48:41 · answer #7 · answered by SAMUEL D 7 · 0⤊ 0⤋
it makes the trig functions easier to deal with... n also in higher calculus, u sometimes need to change the coordinate systems (from rectangular to polar) just to make it a lot more simpler to answer...
2006-08-11 06:36:56 · answer #8 · answered by Toni E 1 · 0⤊ 0⤋
I think we should do away with both and institute the unit "1 revolution".
2006-08-05 14:55:57 · answer #9 · answered by Anonymous · 0⤊ 0⤋
same reason/s y they need mile/s when there is nothing wrong with metre/s
2006-08-05 13:52:59 · answer #10 · answered by Anonymous · 0⤊ 0⤋