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Questions tagged [trigonometry]

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Who first introduced trigonometric substitutions in integral calculus?

I've been researching the history of integral calculus, specifically focusing on the use of trigonometric substitutions. Despite my efforts, it remains unclear who first introduced this technique. ...
Emmanuel José García's user avatar
0 votes
1 answer

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

The Burlet's theorem is a result in Euclidean geometry, which can be formulated as follows: Theorem. Consider triangle $ABC$ with $\angle{C}=\gamma$. Let $P$ be the point where the incircle touches ...
Emmanuel José García's user avatar
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Motivation to extend sin and cos to angles > 90 degree

What was from a historical point of view the motivation to extend the definition of sin and cos to angles larger than 90 degree?
Julia's user avatar
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Did the Maclaurin series for sine and cosine unsettle Indian mathematicians?

As many of you may know, sometime around the 14/15th centuries an Indian mathematician by the name of Madhava of Sangamagrama derived the Maclaurin series for sine and cosine for the first time in ...
voltamatron's user avatar
4 votes
2 answers

Who published the law of tangents first?

The Law of Tangents is a rather obscure trigonometric identity that is sometimes used in place of its better-known counterparts, the law of sines and law of cosines, to calculate angles or sides in a ...
Emmanuel José García's user avatar
1 vote
1 answer

Original source of these 2 trigonometric identities

I am interested in knowing what is the original source/author of the following identities: $\tan{\frac{\alpha}{2}}\tan{\frac{\beta}{2}}+\tan{\frac{\alpha}{2}}\tan{\frac{\gamma}{2}}+\tan{\frac{\beta}{2}...
Emmanuel José García's user avatar
3 votes
0 answers

How were sine and cosine functions computed before the notion of Taylor series?

We know using modern analysis techniques that $\sin x$ and $\cos x$ can be computed by their Taylor series (in fact the Taylor series are given as the definitions of these functions in today's real ...
Maximal Ideal's user avatar
1 vote
1 answer

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

I'm looking for references about trigonometric tables, especially to those with exact values, like Lambert's Algebraische Formeln für die Sinus von drei zu drei Graden. More precisely: Is there an ...
Humberto José Bortolossi's user avatar
1 vote
1 answer

Establishment of relation between angles and sides of a triangle

I was looking for an historical approach to learn about the initiation of trigonometry but got stuck in a part where I have been trying to undestand but couldn't till now. By far, I could learn that ...
MSKB's user avatar
  • 171
2 votes
1 answer

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

The Indian word for what we call sine was 'jyā'. The Surya-siddhanta mentions 'jyā' many many times. As does the Aryabhatiya. In contrast they mention the synonym 'jivā' only once or twice. So why was ...
segar's user avatar
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3 votes
1 answer

Origin of "Inverse Pythagorean Theorem"

There is a lot of information on the history of the Pythagorean theorem, but not much on its closely related cousin; the Inverse Pythagorean Theorem. Would appreciate any resources on the the history ...
Bertrand Einstein IV's user avatar
2 votes
3 answers

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

For various reasons already discussed in other stackexchange posts, we implicitly use radians in trigonometric functions by convention. For example, one period of $sin(x)$ lies in $0 \leq x < 2\pi$,...
BatWannaBe's user avatar
5 votes
1 answer

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

I am reading Carlslaw's "Introduction to the Theory of Fourier's Series and Integrals", first chapter on the history of Fourier series, page 3. The author asserts that Clairaut and Euler did ...
James Warthington's user avatar
6 votes
1 answer

When did trigonometry start using negative numbers?

I'm asking this question looking at the unit circle, and thinking that greek mathematicians didn't use negative numbers. Maybe that can give enough insight into what I'm asking?
A Citizen of The World's user avatar