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Re: Need formulas for arcsin and arctan
From: Lu Abel
Date: 2006 Mar 28, 09:30 -0800

```Whoops, in first paragraph should have said "You get radians by
MULTIPLYING the angle in degrees by 2*Pi/360.

Lu
> We are most familiar with measuring angles in degrees.  Mathematicians
> like to measure them in radians which is a more "natural" unit (for
> example, the formulae for calculating sines and cosines require an angle
> to be measured in radians).  There are 2*Pi radians going all the way
> around a circle, just as there are 360 degrees.  You get radians by
> dividing the angle in degrees by 2*Pi/360.  Your scientific calculator
> will offer the option of expressing angles in either radians or degrees.
>
> On the other hand, regardless of whether an angle is expressed as 45
> degrees or Pi/4 radians, its sine and cosine are the same.   So scanning
> down a table that expresses angles in degrees for a sine or cosine that
> matches your calculation should give you arcsine(x) in degrees.
>
> Lu Abel
>
> Bill wrote:
>
>>> Finally, since arcsine(x) is simply "the angle whose sine is x" scanning
>>> down a conventional table of sines will easily give you the answer to a
>>> degree...
>>
>>
>>
>> Exposing my ignorance (again), arcsine is a bit confusing to me.  Every
>> definition I find in my (old) reference books relates it to an angle in
>>
>> As an analogy, "font" had a specific meeting prior to the computer.  It
>> meant not only a font "family" bit a specific size, weight, slant,
>> compressions or expansion, designer or foundry etc..  12 pt Caslon No.
>> 540
>> Italic was one font, 14 pt Caslon No. 540 Italic another font, as was 36
>> point Bodoni Campanile (Ludlow).  Now "font" is a very loose description,
>> tied mostly to the intellectual-property laws.
>>
>> So my question, is/was "arcsine" a term that applied only to "the angle
>> whose sine is x," in radians, while sin^-1 can apply to whatever system
>> (degrees, rads, grads) one is working in?
>>
>> Thanks
>>
>> Bill
>>
>>
>
>

```
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