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# Questions tagged [trigonometry]

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1 answer
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### 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 ...
1 vote
0 answers
100 views

### 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?
3 votes
0 answers
198 views

### 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 ...
4 votes
2 answers
369 views

### 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 ...
5 votes
1 answer
100 views

### 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 ...
1 vote
1 answer
245 views

1 vote
1 answer
105 views

### 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 ...
2 votes
1 answer
798 views

### 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 ...
3 votes
1 answer
244 views

### 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 ...
6 votes
1 answer
169 views

### 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?