Not at all !
If I want to compute the sinus of 15 degrees, using the series
expansion, I write
X = 15 degrees = 15 * pi/180 = 0.2618
because, 1 degree is just a symbol for the unitless, dimensionless
number pi/180.
I plug this X into the series expansion and get the right result.
Marc
Quoting Clemens Grimm <[log in to unmask]>:
> Zitat von [log in to unmask]:
>
>> Dale Tronrud wrote:
>>> While it is true that angles are defined by ratios which result in
>>> their values being independent of the units those lengths were measured,
>>> common sense says that a number is an insufficient description of an
>>> angle. If I tell you I measured an angle and its value is "1.5" you
>>> cannot perform any useful calculation with that knowledge.
>>
>>
>> I disagree: you can, for instance, put this number x = 1.5 (without
>> units) into the series expansion for sin X :
>>
>> x - x^3/(3!) + x^5/(5!) - x^7/(7!) + ...
>>
>> and compute the value of sin(1.5) to any desired degree of accuracy
>> (four terms will be enough to get an accuracy of 0.0001). Note that
>> the x in the series expansion is just a real number (no dimension, no
>> unit).
>
>
> ... However you get this Taylor expansion under the assumption that
> sin'(0)=1 sin''(0)=0, sin'''(0)=-1, ...
> this only holds true under the assumption that the sin function has a
> period of 2pi and this 'angle' is treated as unitless. Taking e. g.
> the sine function with a 'degree' argument treated properly as 'unit'
> will result in a Taylor expansion showing terms with this unit
> sticking to them.
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