subexpressions (OT: math)

[Gary Herron]

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