7 votes

Why do we still use degrees and cycles if we all implicitly use radians in trigonometric functions?

We do not use radians "by convention". Radian is a necessary intrinsic measure of an angle, which is related to the "fact of nature" that the length of a unit circle is $2\pi$. ...
Alexandre Eremenko's user avatar
6 votes
Accepted

Who was Burlet, the one from Burlet's theorem?

I am unable to find any references to a "theorem of Burlet" in a print publication regardless of language, e.g. Satz von Burlet, théorème de Burlet. All online resources referencing this ...
njuffa's user avatar
  • 6,496
5 votes
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Original source of these 2 trigonometric identities

After hours of searching through scans of books from the 18th and 19th centuries in English, German, French, Italian, Spanish, and Latin I managed to find a source for each of the two identities. The ...
njuffa's user avatar
  • 6,496
5 votes
Accepted

Who published the law of tangents first?

I agree that the reference in Wikipedia seems at first sight to be off. But if one reads a little further into p.184 (frame 192 of 401 in the archive.org display) of vol.2 of Roshdi Rashed (ed.) 1996, ...
terry-s's user avatar
  • 4,375
4 votes

Etymology of 'sine'. The Arabic 'jayb' and 'jiba' derive from the Sanskrit 'jivā' ... but why not from the more common Sanskrit 'jyā'?

The unabridged Oxford English Dictionary, which is quite authentic does not trace sine to any Sanskrit words " Etymology: < Latin sinus a bend, bay, etc.; also, the hanging fold of the upper ...
AChem's user avatar
  • 4,049
3 votes

Who published the law of tangents first?

The law of tangents is indeed attributed to the Danish polymath Thomas Fincke (1561–1656). According to his short biography by Jürgen Schönbeck (in German and behind a paywall), the law appears in Vol....
Tom Heinzl's user avatar
3 votes

History of trigonometric tables including Lambert's Algebraische Formeln für die Sinus von drei zu drei Graden

This is a partial answer that focuses on the second part of the question. The author of J. H. Lambert, "Algebraische Formeln für die Sinus von drey zu drey Graden", In J. H. Lambert, ...
njuffa's user avatar
  • 6,496
3 votes

Establishment of relation between angles and sides of a triangle

Trigonometry was developed for the needs of astronomy. So originally this was not the plane trigonometry that we study at school but spherical trigonometry. The main (and almost only) source that ...
Alexandre Eremenko's user avatar
3 votes

Where could I find the reference for the statement of Euler finding out the coefficients of Fourier series?

Euler's calculation of Fourier series coefficients appears in his paper De serierum determinatione seu nova methodus inveniendi terminos generales serierum from 1753. A link to it on the Euler ...
KCd's user avatar
  • 5,312
3 votes
Accepted

When did trigonometry start using negative numbers?

Seventeenth century mathematicians were still hesitatnt to use negative numbers even when it came to Cartesian coordinates. According to Tannery: "One frequently attributes wrongly to Descartes ...
Conifold's user avatar
  • 75.2k
2 votes

Origin of "Inverse Pythagorean Theorem"

Seems to be pretty commonplace as well as having multiple names. Here's an article which references some other article, both relatively recent.
Carl Witthoft's user avatar
1 vote
Accepted

Why do we still use degrees and cycles if we all implicitly use radians in trigonometric functions?

I ran across an answer to my satisfaction, but it sort of turns the question on its head: "Why do we implicitly use radians in trigonometric functions if we still use degrees and cycles?" It'...
BatWannaBe's user avatar

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