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### Where does sine come from?

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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
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?
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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,
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
```
Associated Topics:
High School History/Biography

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