Questions tagged [trigonometry]
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19 questions
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How were trig tables calculated, historically?
how were trig tables calculated, prior to electronics? Prior to calculus?
Is there an algorithm, like with roots?
Googling online, I see talk about either using Taylor series or some tricks with half ...
- 11
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Giza pyramids and convergents of √φ/2 — known connection?
The three main Giza pyramids have height/base ratios that are exact in royal cubits:
Pyramid
Height
Base
Ratio
Khufu (Great)
280
440
7/11
Khafre
274
411
2/3
Menkaure
125
200
5/8
These are the 4th, 5th,...
- 143
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How did Eratosthenes measure the angle of the sun wrt. the vertical?
It is often mentioned that Eratosthenes used the length of a gnomon's shadow to calculate the radius of the Earth. To me this necessarily implies using a trigonometric table to find the corresponding ...
- 121
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How did Roger Cotes come up with the idea of radian measure?
What was the problem that Roger Cotes was trying to solve that he came up with the idea of radian measure? Was he trying to find a suitable unit of angle measure so that the derivative of $\sin x$
is ...
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Before logarithms, were tables of half trigonometric functions published so multiplications could be calculated by addition using prosthaphaeresis?
When trigonometric hand calculations were vitally important, for example in navigation, some tables included more "exotic" trig functions such as the versed sine or versine (one minus cos) ...
- 282
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255
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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. ...
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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 ...
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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?
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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 ...
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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 ...
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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}...
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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 ...
- 453
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1
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172
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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 ...
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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 ...
- 171
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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 ...
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