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Bill:

I'm an engineer by training and about to collect social security, so my
math education significantly predates pocket calculators and home
computers.  "arcsine(x)" simply meant (and still means) "the angle whose
sine is x"   You got your choice of how to express the angle -- radians,
degrees, grads, whatever.   In fact, I believe I was introduced to
arcsine in high school trig but didn't learn of radians until college.
For some strange reason (perhaps either because the formulae for
calculating trig functions require radians as input or to force a common
notation), the trig functions in many early computer programs used
radians.  That can show up even today.  I just tried Window's calculator
and it's happy returning arcsine(0.5) as 30 degrees if I've set angle
notation to degrees, but Excel returns it only as Pi/6 and Excel's help
clearly says "it's up to you to convert to degrees if you want it that way."

So, no, I'm not aware of a pre-computer "standard" that said arcsine was
expressed in radians.

Lu Abel

Bill wrote:
> Lu wrote:
>
>
>>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.
>
>
>>Whoops, in first paragraph should have said "You get radians by
>>MULTIPLYING the angle in degrees by 2*Pi/360.
>
>
> I am sorry, I did not express myself clearly.  I understand the conversion
> from degrees to rads to grads, and why engineers etc. find radians more
> convenient.
>
> What I am trying understand:  Is "arcsine" the *exact* equivalent of "sine
> ^-1" outside the kingdom of the pocket calculator today?  Specifically, it
> seems "arcsine" was the angle in radians.  If so, has that changed?
>
> For example, several decades ago--unless you could walk or stand on
> water--you could not walk or stand on a "dock."  (Hence the term "dry
> dock").  Gourmet was a noun, not an adjective.  Was arcsine exclusively
> refering to angle in radians, and is that the case or not today?
>
> Thanks again
>
> Bill
>
>

   

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