Ahmad ibn ‘Abdallah Habash Hasib Marwazi (766 – d. after 869 in Samarra, Iraq ) was a Persian astronomer, geographer, and mathematician from Merv in Khorasan who for the first time described the trigonometric ratios: sine, cosine, tangent and cotangent.
He flourished in Baghdad, and died a centenarian after 869. He worked under the Abbasid caliphs al-Ma’mun and al-Mu’tasim.
He made observations from 825 to 835, and compiled three astronomical tables: the first were still in the Hindu manner; the second, called the ‘tested” tables, were the most important; they are likely identical with the “Ma’munic” or “Arabic” tables and may be a collective work of al-Ma’mun’s astronomers; the third, called tables of the Shah, were smaller.
Apropos of the solar eclipse of 829, Habash gives us the first instance of a determination of time by an altitude (in this case, of the sun); a method which was generally adopted by Muslim astronomers.
In 830, he seems to have introduced the notion of “shadow”, umbra (versa), equivalent to our tangent in trigonometry, and he compiled a table of such shadows which seems to be the earliest of its kind. He also introduced the cotangent, and produced the first tables of for it.