Subject: Re: [HM] origin of trigonometric identities
From: Kim Plofker (Kim_Plofker@Brown.edu)
Date: Wed May 17 2000 - 00:09:28 EDT
> Does anyone know the origin of the sum and difference of angles
> identities,. i.e., sin(A+/-B) and cos(A+/-B)? In an article in the
> American Journal of Science and Arts (1819), American mathematician
> Theodore Strong gives "an improved method of obtaining" these
> formulas, but it is not clear if the formulas are new or just his
> method of deriving the formulas.
>
> Todd Timmons
Well, the rule for the sine of the sum (and by implication, the
cosine too) appears in the "jyotpatti" or "sine-demonstrations"
of Bhaskara (II) in around 1150, which predates Dr. Strong by a while.
They're not necessarily Bhaskara's inventions, but they are likely
not more than a century or so earlier. They must have been known in the
Islamic developments of Indian trigonometry (though I can't find a
specific Arabic source just now) and reached Europe from there. So
I think Dr. Strong's "improved method" must just have referred to his
original derivation; it's hard to believe that he would have thought the
formulas themselves were new.
With best wishes,
Kim Plofker
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