Talk:Trigonometric functions: Difference between revisions

Revision as of 22:40, 25 March 2004

Revision as of 23:06, 25 March 2004

Line 48:

::It was Robert of Chester's translation from the Arabic that resulted in our word "sine." The Hindus had given the name ''jiva'' to the half-chord in trigonometry, and the Arabs had taken this over as ''jiba''. In the Arabic language there is also the word ''jaib'' meaning "bay" or "inlet." When Robert of Chester came to translate the technical word ''jiba'', he seems to have confused this with the word ''jaib'' (perhaps because vowels were omitted); hence, he used the word ''sinus'', the Latin word for "bay" or "inlet." Sometimes the more specific phrase ''sinus rectus'', or "vertical sine," was used; hence, the phrase ''sinus versus'', or our "versed sine," was applied to the "sagitta," or the "sine turned on its side."

:(Note that the "versed sine" is 1–cos(&theta). I'm guessing that ''rectus'' and ''versus'' here refer to what we would now call the ''y'' and ''x'' coordinates, assuming that they originally drew a circle and measured the angle from the horizontal...Boyer doesn't say, however.) [[User:Stevenj|Steven G. Johnson]] 21:55, 25 Mar 2004 (UTC)

:By the way, assuming an etymology of ''sinus'' for sine because of the "curvaceous shape" of the sine (from the other meaning of ''sinus'' for "curve," in particular the curved shape of a draped toga or garment) is probably an anachronism. Plots of the sine function ala analytic geometry didn't come until centuries after Chester. On the other hand, Chester may have mistakenly thought that "bay" alluded to the subtended arc; I'm just speculating, though. [[User:Stevenj|Steven G. Johnson]] 22:18, 25 Mar 2004 (UTC)

:(Note that the "versed sine" is 1–cos(&theta). I'm guessing that ''rectus'' and ''versus'' here refer to what we would now call the ''y'' and ''x'' coordinates, assuming that they originally drew a circle and measured the angle from the horizontal...Boyer doesn't say, however. Further evidence for this is the fact, according to the OED, that "sagitta", originally a synonym for the versed sine, is also an obsolete synonym for [[abscissa]]. ''sagitta'' is Latin for "arrow", and according to the OED's citations this is a visual metaphor for the versed sine (if you see the arc as the bow, the chord as the string, and the versed sine as the protruding point of the arrow shaft.) Note that Wikipedia could use a short entry on [[versed sine]]. [[User:Stevenj|Steven G. Johnson]] 21:55, 25 Mar 2004 (UTC)