2006-12-08 04:22:48 · 6 answers · asked by x_squared 4 in Science & Mathematics ➔ Physics
Radians are used in calculus, unless otherwise noted.
This is because derivatives of trig functions are nice and neat if the variable is measured in radians. It gets messy if you're dealing in degrees.
The derivative of sin(x) is only cos(x) if x is measured in radians because the definition of the derivative comes down to:
cos (x) times lim (delta x->0) of sin (delta x) / delta x.
That limit equals 1 only when we're in radians. If you are dealing in degrees, that limit becomes (pi/180), so the derivative of sin(x) is (pi/180)* cos (x), which is not as "friendly" as the derivative in radians. Especially in higher order derivatives.
Hope this helps :)
2006-12-08 04:45:37 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Radians are the 'natural' way to measure an angle. The series expressions for all trig functions use radians. The polar form of a complex number uses radians.
If someone tells you that and arc on a circle of radius 2 has an angle of 90 deg, how do you find the length of the arc? If you use radians then
90 deg = pi/2
arc length = (pi/2)*2 = pi, which will have the same units as the radius.
Now, how would you do the same calculation using degrees?
2006-12-08 04:37:12 · answer #2 · answered by modulo_function 7 · 0⤊ 0⤋
Radians have no units. Because of their relationship to the unit circle (ie arclength) they provide the best choice for approximations using polynomial expansions.
You can recognize that you must use radians by dimensional analysis. If you use degrees, you get units which you shouldn't because sin(x) has no units. Otherwise you would encounter difficulty saying y=r*sin(theta)
2006-12-08 05:00:22 · answer #3 · answered by omnigoddess_althena 2 · 0⤊ 0⤋
We use radians because the series we get as a result is much nicer and cleaner than if we used degrees. I would assume that you are using radians unless told otherwise.
2006-12-08 04:31:01 · answer #4 · answered by msi_cord 7 · 0⤊ 0⤋
on your calculator, you will detect a button marked DRG. D is levels R is radians G is grads Press the button till at last Rads shows interior the demonstrate. enter 0.1943. Press INV or 2d function, or sin^-a million counting on your calculator. the respond is now given in radians. continually verify which mode your calculator is in {D, R, or G} in the previous you start up any trigonometrical calculations desire this helps, Twiggy.
2016-12-30 03:36:39 · answer #5 · answered by ? 3 · 0⤊ 0⤋
Forget about degrees, there for dummies, always use radians.
2006-12-08 04:27:56 · answer #6 · answered by Anonymous · 0⤊ 0⤋