subexpressions (OT: math)

[Steven D'Aprano]

On Sun, 03 Jun 2007 11:26:40 -0700, Stebanoid at gmail.com wrote:

> if you are discordant read more :P :
> sine is a dimensionless value.
> if we expand sine in taylor series sin(x) = x - (x^3)/6 + (x^5)/120
> etc.
> you can see that sin can be dimensionless only if x is dimensionless
> too.
> 
> I am a professional physicist and a know about what I talk

I am confused why you get different results for the square root of an
angle depending on whether you use degrees or radians:

sqrt(25°) = 5° = 0.087266462599716474 radians
sqrt(25*pi/180) = 0.66055454960100179 radians

If angles are dimensionless numbers, then:

degrees_to_radians(sqrt(25°)) 

should equal 

sqrt(degrees_to_radians(25°))

but they don't.

How do you interpret the square root of an angle? What does it mean?


-- 
Steven.