Re: History of trigonometry

Nick schrieb:

Ken Pledger wrote in message

zeros wrote:

....
When did someone define the sine of an angle greater than 90 degrees?

I think this may be happened in 17c. But I can't find any record about my
question....


It's an interesting question, which most popular historians of
mathematics scarcely mention.

In fact, http://www-history.mcs.st-andrews.ac.uk/Biographies/Euler.html says
that:

"He made large bounds forward in the study of modern analytic geometry and
trigonometry where he was the first to consider sin, cos etc. as functions
rather than as chords as Ptolemy had done."

http://www-history.mcs.st-andrews.ac.uk/HistTopics/Trigonometric_functions.html#76
says that:

"The first actual appearance of the sine of an angle appears in the work of
the Hindus."

"Chapters of Copernicus's book giving all the trigonometry relevant to
astronomy was published in 1542 by Rheticus. Rheticus also produced
substantial tables of sines and cosines which were published after his
death. In 1533 Regiomontanus's work De triangulis omnimodis was published.
This contained work on planar and spherical trigonometry originally done
much earlier in about 1464. The book is particularly strong on the sine and
its inverse."

In antiquity and around the world the chords in circles are observed
and sometimes with relation to the angle or the arc. Now as the chord
is twice the sin, first the sin was called half chord and the cos is
the distance of the chord from the center of the circle.

You mention astronomy and map making. The developement of log-tables
was originating with sin-tables. Now here i have a gap in my knowledge.
But before Euler in 1714 Roger Cotes discovered.
ln[cos(@) + sqrt ( - 1) * sin(@)] = sqrt ( - 1) * @
http://www.mathpages.com/home/kmath192/kmath192.htm

With friendly greetings
Hero

.

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