alBiruni
alBattani

Trigonometry
AlBiruni was among those who laid the foundation for modern Trigonometry. He was a philosopher, geographer, astronomer, physicist and mathematician. Six hundred years before Galgeo, AlBiruni discussed the theory of the earth rotating about its own axis.
AlBiruni carried out geodisic measurements and determined the earth's circumference in a most ingenious way.
With the aid of mathematics, he enabled the direction of the Qibla to be determined from anywhere in the world. In the domain of trigonometry, the theory of the functions; sine, cosine, and tangent was developed by Muslim scholars of the 10th century. Muslim scholars worked diligently in the development of plane and spherical trigonometry.
The, trigonometry of Muslims is based on Ptolemy's theorem but is superior in two important respects: it employs the sine where Ptolemy used the chord and is in algebraic instead of geometric form.
What
is Taught:
The Greeks were the developers
of trigonometry.
What
Should be Taught:
Trigonometry remained
largely a theoretical science among the Greeks.
It
was developed to a level of modern perfection
by Muslim scholars, although the weight of the
credit must be given to alBattani.
The
words describing the basic functions of this science,
sine, cosine and tangent, are all derived from
Arabic terms. Thus, original contributions by
the Greeks in trigonometry were minimal.
Abul
Wafa
9th Century
What is Taught:
During the 17th century Rene Descartes made the discovery that Algebra could be used to solve geometrical problems. By this, he greatly advanced the science of Geometry.
What Should be Taught:
Mathematicians of the Islamic Empire accomplished precisely this as early as the 9th century A.D. Thabit bin Qurrah was the first to do so, and he was followed by Abu'l Wafa, whose 10th century book utilized Algebra to advance Geometry into an exact and simplified science. 