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Comment by throwawayffffas | Hacker News Reader

Well I don't think they are. Sure they make computing the function simpler. But I would hazard that most people that use these functions are not doing geometry and they are already working with radians. In short if you give any kind of engineer working on any kind of signal processing domain a sine function where sin(1) = 0 you are only going to confuse them.

PS: that's why mathematicians don't use turns they are mostly not doing geometry and radians in that case typically make for better formulas.

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> sin(1) = 0 you are only going to confuse them.

Not really, pretty much every single one would assume you just forgot the pi, because everyone writes “sin(1pi)” and never actually “sin(3.14…)” because no one ever writes down numbers in the unit of radians, they already convert to half rotations or full rotations by scaling with pi. Imagine if someone went “nanometers are a dumb unit, because I always write down my numbers as h=342 x 10^-9m” that last part “10^-9m” is just nm. In the same way that sin(1.432pi) might as well just be written sin(1.43*rotation). Arguing for radians is arguing that the most natural way to write it is sin(8.985). Which you will pretty much never see anyone do.

In my example you would not actually write it out but instead have something like this.

[sin(x) for x in sample]

My point is that the trig functions are abstract and useful in multiple domains and in most of these domains turns does not make sense. Turns only makes sense in geometry and maybe some physics but most of the time in these cases you might be better off working with other units, like say quaternions.

The fact is in the vast majority of literature trig functions take rads as arguments, it's the sane default for that reason alone.

To clarify my objection is with this statement

> no one ever writes down numbers in the unit of radians, they already convert to half rotations or full rotations by scaling with pi

That statement is true only if you are talking about geometry, If you are working in any other domain the trigonometric functions operate on real numbers and have nothing to with rotations or angles and if I call sin(1) I expect to get back 0.7847 not 0

Still, the discussion is only about convenience. For example, e^ix = cos x + i sin x (with sin/cos taking an argument in radians) would become e^ix = cos 2pi x + i sin 2pi x (with sin/cos taking an argument in turns). It's more cumbersome than the radian-based definitions, but it's not strictly different.

As mentioned elsewhere in this thread, with turn-based rotation units, this relationship can be simplified to avoid transcendental numbers entirely:

> (-1)^(2x) = cos(x) + i sin(x)

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