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### Origin of the Terms Sine and Cosine

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Date: 07/02/97 at 05:54:38
From: Kel
Subject: Origin of terms sine and cosine

Hi -

I have a history question about trigonometry:

I assume the term tan comes from the word tangent, and I understand
why, but where do the terms sine and cosine come from?

Thanks, Kel
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Date: 07/08/97 at 12:35:33
From: Doctor Chita
Subject: Re: Origin of terms sine and cosine

Hi Kel,

According to Howard Eves, in his book "In Mathematical Circles" (page
80), the word sine has its origin in ancient Hindu Arabic mathematics,
circa 2,000 years ago. The Arabs called it "ardha-jya" meaning "half-
chord" and then abbreviated it to "jya" meaning "chord." Phonetically,
this last word was shortened to "jiba" and later, the vowel was
eliminated and it ended up as "jb" a meaningless word in Arabic.
Later translators substituted the word "jaib" containing the same
letters but which means "cove" or "bay."

When Gherardo of Cremona came across the word in about 1150, he
translated it to its Latin equivalent "sinus" which eventually became
our familiar "sine."

Of course, "cosine" follows naturally, since it means "the sine of the
complement" of an angle (as in cotangent and cosecant.)

The half-chord idea can be seen if you draw a unit circle with two
radii forming an acute angle at the center. Drop a perpendicular
segment from the endpoint of one radius on the circle to the other
radius. This creates a right triangle with a radius as a hypotenuse.
The perpendicular leg from the circle is one-half of a chord. It also
is the sine of the angle at the center.

-Doctor Chita,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
High School Trigonometry

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