subexpressions (OT: math)

[stef]

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