Where does sine come from?

Date: 6 Jan 1995 12:23:18 -0500
From: Patty Wu
Subject: (none)

Dear Dr. Math, 

        Hi! I'm a student from Internet, and I'm doing a reserch on Ask 
Dr. Math. What I need to do is to ask a question to Dr. Math, and get a 
response. So could you please answer my question? That would help 
me a lot. Thanks in advance.

        The question is - Who is the inventor of Sin? And when did 
he/she discover it? Also, how did he/she do it?

Date: 6 Jan 1995 17:29:10 -0500
From: Anonymous
Subject: Re: Origin of Sine

Hi Patty!

      According to my Math History book ("A History of Mathematics," 
by Carl Boyer), the concept of the sine came from India.  The first mention 
of it that we know of is in a series of books called the Siddhantas, literally
"Systems" (of astronomy).  They were written around the year 400, 
supposedly by Surya, the Sun god.   Already, Greek Mathematicians had 
studied the relationship between the lengths of chords of a circle and the 
angles of the circle that they cross.  What is significant about what was 
done in India is that they started looking at the relationships between 
half-chords and the halves of the angle that the whole chord would cross.  

      Draw the chord of a circle and the angle of the circle that it crosses,
and then bisect both--can you see why the relationship between the 
half-chord and the half-angle is the Sine?

   Through a mistranslation from Arabic to Latin, somehow the Indian 
word for this relationship, jiva, became our word sine.

      Later, in the 1700s, through the work of the mathematician Euler, 
sine came to mean a ratio, not merely the length of a certain line.

I hope this helps!

                              Elizabeth, a math doctor