Gary Herron wrote:
> Wildemar Wildenburger wrote:
>
>> Gary Herron wrote:
>>
>>
>>> Of course not! Angles have units, commonly either degrees or radians.
>>>
>>> However, sines and cosines, being ratios of two lengths, are unit-less.
>>>
>>>
>>>
>>>> To understand it: sin() can't have dimensioned argument. It is can't
>>>> to be - sin(meters)
>>>>
>>>>
>>>>
>>>>
>>> No it's sin(radians) or sin(degrees).
>>>
>>>
>>>
>> NO!
>> The radian is defined as the ratio of an arc of circumfence of a circle
>> to the radius of the circle and is therefore *dimensionless*. End of story.
>> http://en.wikipedia.org/wiki/Radian and esp.
>> http://en.wikipedia.org/wiki/Radian#Dimensional_analysis
>>
>> *grunt*
>>
>>
> No, not end-of-story. Neither of us are being precise enough here. To
> quote from your second link:
> "Although the radian is a unit of measure, it is a dimensionless
> quantity."
>
> But NOTE: Radians and degrees *are* units of measure., however those
> units are dimensionless quantities , i.e., not a length or a time etc.
>
> The arguments to sine and cosine must have an associated unit so you
> know whether to interpret sin(1.2) as sine of an angle measured in
> degrees or radians (or whatever else).
>
> Gary Herron
>
>
>
Sorry about entering the discussion so late,
and not sure I repeat one of the messages.
But can't we see it this way:
radians / degrees (which one 360 or 400) are just mathematical
scaling factors,
like kilo, mega etc.
If a wheel is turning around at
2*pi*100 [rad /sec]
does something physical change is we leave the radian out
the wheeel is turning at
100 [1/sec]
No it's now called frequency, and has just some different scaling.
SQRT of "rad/sec" ?
Yes, in electronics the noise density is often expressed in [nV/SQRT(Hz)]
cheers,
Stef Mientki
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