[Even though this question may seem as a duplicate of this question about the History of sine function, I'd like to ask it again - with a more specific title and a more specific focus (on specific references) which hopefully will re-attract some users.]


The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse and this is the mental picture one must have in mind:

enter image description here

This or similar pictures can be found in many ancient texts on trigonometry.

But today, when hearing "sine" many people inevitably have in mind a mental picture like this:

enter image description here

and it's not so hard to understand how it arises from the first picture (by rotating the radius with constant speed and plotting the sine):

enter image description here

This was not always so: neither has there been this mental picture of the sine function nor have there been physical drawings.

My question is:

What are the earliest (known) physical drawings of the plot of the sine or another trigonometric function?

Are they Greek, Indian, Chinese or from the Middle Ages? A specific reference would be welcome.


This may not be the earliest reference, but it's a rather early one, as I suppose:

enter image description here

(Albrecht Dürer: Underweysung der Messung, mit dem Zirckel und Richtscheyt, in Linien, Ebenen unnd gantzen corporen, 1525)

  • Very closely related, and possible a duplicate --- History of sine function – Dave L Renfro Nov 5 at 11:02
  • Thanks to @DaveLRenfro: I found an explicit reference in this answer: de.wikisource.org/wiki/… (which may not be the earliest known plot). – Hans Stricker Nov 5 at 11:24
  • If Alexandre and Mauro’s answers could be moved (or repeated) here, perhaps we might best close the other question, which was only for sine and whose author apparently never even returned to read the answers. Boyer (1947) mentions early graphs by Roberval (c.1635), Wallis (1670), Cotes (1722). – Francois Ziegler Nov 5 at 12:14
  • Possible duplicate of History of sine function – José Carlos Santos Nov 6 at 8:51
  • @JoséCarlosSantos: Please see the "discussion" that already took place. – Hans Stricker Nov 6 at 8:57

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