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Why not just work with everything in degrees? Why are radians so much better in higher level math. I use radians all the time, but I just don't see the big deal.

2007-12-19 06:12:53 · 4 answers · asked by de4th 4 in Science & Mathematics Mathematics

4 answers

the number 360 is pretty arbitrary. (although for the ancient Babylonians who developed trigonometry, 360 was a nice "round" number in their base-60 enumeration system.)

Radians are a measure that is connected to the geometry of the circle. For a unit circle, the measure of the angle is equal to the length of the arc the angle subtends. That's a logical way to measure angles.

ALL calculus trig formulas are expressed in radians, because they take an algebraically simpler form that way. And the reason for that simpler form is the geometric connection I just mentioned.

After some experience with radians, the question you'll be asking is "why in the world would anyone work with degrees? radians are much simpler!"

2007-12-19 06:35:24 · answer #1 · answered by Michael M 7 · 0 0

As several other posters have suggested, radians are much more natural.

If an angle is expressed in radians, then you can write the Taylor Series of sin, cos, tan, etc. (which algebraically is considered by some to be their definitions) in a very natural way, e.g.

sin(x) = x - x^3/3! + x^5/5! - x^7/7! +...
etc.

if you were using degrees instead, you'd get

sin(x) = π/180*x - (π/180*x)^3/3! +(π/180*x)^5/5! -...

If you ask me the fist way makes a lot more sense than the second way. Degrees are used for historical reasons. Radians are used for mathematical ones.

2007-12-19 15:37:23 · answer #2 · answered by mnost1 3 · 0 0

Radians make life a lot simpler, since they are in some sense a "natural" unit. This is because a unit circle (a circle with radius of one) has a circumference of 2*pi. The number of length units in its circumference is equal to the number of radians around the circle. If I want to know how long an arc of such a circle is, it is the same number of units as radians in the angle. Since the unit circle is used so much, it's much more convenient to use radians rather than having to convert all the time for degrees.

2007-12-19 14:17:17 · answer #3 · answered by smcwhtdtmc 5 · 0 1

Radians are handy for relating distance along the circle relative to the size of the circle. It relates to pi. 2*pi radians go all the way around the circle.

2007-12-19 14:23:40 · answer #4 · answered by A Guy 7 · 0 0

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