Trigonometry he systematically employed the trigonometric function sine

Trigonometry

Trigonometry terms has been taken from the Greek, Trigonon,
which means triangle and the other word, metron, has the meaning of measure.
The trigonometry is the connection link between the way calendars are
calculated, for the astronomy and mathematics, the sundial, and also the Gnomon.
In the Islamic world, the calculation of the spherical triangles was necessary
to carry out the ritual custom. The direction to Mecca (qibla) was
indicated that the next to the hour lines on all public sundials.

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Muslim mathematicians have been contributed in this trigonometry
fields. For a long time, the chord was used along with the sine. The magnitude
theory has been found in the al-Battani work around 858-929 CA. In his
astronomical work Islah al-Majisti (The Perfection of the Almagest), he
systematically employed the trigonometric function sine and versed sine with
arguments between 0? and 180?. Since the cosine is defined as the sine of the
complement of the angle and since no negative numbers are used, the versed sine
is defined in the second quadrant as a sum of two quantities.

The elements of trigonometry are set forth in an even more
systematic way in the Kitab al-Kamil (Perfect Book) of Abu I-Wafa
(940-997/998). He defined several trigonometric functions in the circle with
radius 1. The trigonometric tangent function is defined as a line on a tangent
to the circle.

The proof of the general spherical sine theorem was given by Abu
I-Wafa in his al-Majisti (Almagest), by his pupil Abu Nasr ibn Iraq (d.
1036) in Risala fi ma’rifa al-qisi al-falakiyya (Treatise on the
Determination of Celestial Arcs), and by al-Khujandi, in the Kitab Maqalid
‘ilm al-hay’a (Book on the Keys of Astronomy).

The use of trigonometry was expended through al-Biruni (973-1048).
He is the author of the Mas ‘udic Canon, which is a summary of the
results from the works of many predecessors and of personal observations and
calculations. It comprises 11 books. Book 3 is dedicated to trigonometry.

Another important scholar in the area of trigonometry was Nasir
al-Din al-Tusi (1201-1274). He wrote Kitab al-shakl al-qatta’ which
means The Book of the secant figure, also known as Treatise on the Complete
Quadrilateral. It was written in Persian and translated by the author into
Arabic in 1260 possibly for the needs of the observatory of Maragha. While in those
five books have contains a full system of trigonometric formulas for the plane
and spherical triangles. This work played an important role in the development
of mathematics in Europe.

 

Algebra:

            The word “Algebra”
is derived from the Arabic language ?????
(Al-Jabr) which means the completion or “reunion of broken
parts” and throve during the Islamic golden age (especially in the year
830). Algebra comes from the treatise by the medieval Persian mathematician,
Muhammad Ibn Musa Al-khwarizmi, who wrote a book with Arabic title, Kit?b
al-mu?ta?ar f? ?is?b al-?abr wa-l-muq?bala, which can be translated as “The
Compendious Book on Calculation by Completion and Balancing”. The treatise
provided for the systematic solution of linear and quadratic equations. The
word al-jabr, presumably has meant restoration or completion and refer to the
transposition of subtracted terms to the other side of an equation. The word muqabalah
is said to refer to reduction or balancing that is the cancellation of like
terms on opposite sides of the equation. Al-Khwarizmi describes the term of the
operations that was introduced reduction and balancing, by following to the
transposition of subtracted terms to the other side of an equation, which means
the cancellation of like terms on opposite sides of the equation.

Algebra originally can be traced back to ancient of Babylon which
has been developed a fairly complicated mathematical system in which case they
were able to calculate in a similar way to algebra nowadays. Using this system,
they are able to apply formulas and compute solutions for unknown values ??for
problem classes that are usually solved by using Linear equations, Quadratic
equations and Indefinite Linear Equations. In contrast, the Egyptians and most
of the Indian, Greek, and Chinese peoples in the first millennium, they are usually
still using geometrical methods to solve such equations, such as those
mentioned in “the Rhind Mathematical Papyrus”, “Sulba
Sutras”, “Eucilid’s Elements “And” The Nine Chapters on the
Mathematical Art “. The result of the Greeks in Geometry has been written
in the book of elements, provides a framework for generalising the formula of
mathematics beyond the specific solution of a particular problem into the more
general system of expressing and solving equations, i.e. the framework of the
deduction logic of thought.

Besides Al-Khwarizmi, many other figures also have been developed
in Algebra theorem. Among others are:

Al-Qalasadi: introduce algebraic symbols. The symbols were
developed in the 14th century by Ibnu al-Banna. Then, in the 15th
century, Al-Qalasadi has been developed this. Al-Qalasadi has introduced the
mathematics symbols which use the characters of Arabic alphabet.

Sharaf al-D?n al-Muzaffar ibn Muhammad ibn al-Muzaffar al-??s?
(1135-1213) is a Mathematician and Islamic Astronomer from Persian. Sharif
al-Din has been taught the various topics such mathematics, astronomy and
related fields like numbers, astronomical tables, and astrology. Al- ??s? has
been written several papers on Algebra. He gave the Ruffini-Horner methods to approach the
roots of cubic equations. Although this method had previously been used
by Arab mathematicians to find almost the nth root of an integer, al- ??s? was the first to apply this method to solve
this general equation. In Al-Mu’adalat (About Equations), al-??s? finds
algebraic and numerical solutions of cubic equations and which first finds a
cubic polynomial derivative, an important result in differential calculus.

Omar Khayyam, a Persian scientist who has been developed the
algebra of geometry and found the general shape of the geometry of the cubic equation.

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