Where did the words sine, cosine and tangent originate from? What do they mean?

Question

Where did the words sine, cosine and tangent originate from? What do they mean?

Answer 1

Sine, cosine and tangent are trigonometric ratios.

Trigonometric functions were studied by Hipparchus of Nicaea (180–125 BC), Ptolemy of Egypt (90–165 AD), Aryabhata (476–550), Varahamihira, Brahmagupta, Muḥammad ibn Mūsā al-Ḵwārizmī, Abū al-Wafā' al-Būzjānī, Omar Khayyam, Bhāskara II, Nasir al-Din al-Tusi, Ghiyath al-Kashi (14th century), Ulugh Beg (14th century), Regiomontanus (1464), Rheticus, and Rheticus' student Valentin Otho. Etymologically, the word sine derives from the Sanskrit word for half the chord, jya-ardha, abbreviated to jiva. This was transliterated in Arabic as jiba, written jb, vowels not being written in Arabic. Next, this transliteration was mis-translated in the 12th century into Latin as sinus, under the mistaken impression that jb stood for the word jaib, which means "bosom" or "bay" or "fold" in Arabic, as does sinus in Latin.[2] Finally, English usage converted the Latin word sinus to sine.[3] The word tangent comes from Latin tangens meaning "touching", since the line touches the circle of unit radius

Sine

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

Cosine

The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Tangent

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

Answer 2

Sine The name sine came to us from the Latin sinus, a term related to a curve, fold, or hollow. It is often interpreted as the fold of a garment, which was used as we would use a pocket today. The use in mathematics probably comes about through the incorrect translation of a Sanskrit word. Here is a brief description of how that came about from Passage to China by Amartya Sen. "In his Sanksrit mathematical treatise completed in 499 AD, Aryabhata used jya-ardha (Sankscrit for “chord half”), shortened later into jya, for what we now call “sine.” Arab mathematicians in the eighth century transliterated the Sanskrit word jya into the proximate sound of jiba and then later changed it into jaib (with the same consonants as jiba), which is a good Arabic word, meaning a bay or a cove, and it was this word that was later translated by Gherardo of Cremona (circa 1150) into its equivalent Latin word for a bay or a cove, viz., sinus, from which the modern term “sine” is derived."

COSINE was originally written "co.sine," short for COMPLEMENTI SINUS:

the sine of the complement. The COSINE of angle AOB is the sine of the

complementary angle (ABO in the figure). Likewise COTANGENT and

COSECANT are the tangent and secant respectively of the complementary

angle.

TANGENT comes from the Latin TANGENS, the present participle of TANGERE,

"to touch." In other words, it means "touching." It was originally

applied to the line segment AB in the figure: the segment of the

tangent to the circle at A that is cut off by the extension of OB. The

ratio of the tangent AB to the radius of the circle, OA, is the

TANGENT of angle AOB.

:)

Answer 3

These trigonometric functions are said to be discovered and improved by Hipparchus of Nicaea (180–125 BC), Ptolemy of Egypt (90–165 AD), Aryabhata (476–550), Varahamihira, Brahmagupta, Muḥammad ibn Mūsā al-Ḵwārizmī, Abū al-Wafā' al-Būzjānī, Omar Khayyam, Bhāskara II, Nasir al-Din al-Tusi, Ghiyath al-Kashi (14th century), Ulugh Beg (14th century), Regiomontanus (1464), Rheticus, and Rheticus' student Valentin Otho...

Sine ---:>   Sinus(a latin word) ---:>   Fold ....

Tangent ---:>   Tangens ---:>   Touching ...

Secant ---:>   Secans ---:>   Cutting ...