A mathematician from Nayriz, a town near Shiraz. He flourished between ca. 875 and ca. 940. Little is known of his life but we do know that he dedicated some of his works to Caliph al-Mu'tadid (reigned 892-902) so he almost certainly moved to Baghdad and worked there for the caliph. He wrote commentaries on work by Ptolemy and Euclid, compiled astronomical tables, wrote a book for al-Mu'tadid on atmospheric phenomena. Al- Nayrizi's commentaries on Ptolemy and Euclid were translated into Latin by Gerard of Cremona. He used the so-called umbra (versa), the equivalent to the tangent, as a genuine trigonometric line. He wrote a treatise on the spherical astrolabe, which is very elaborate and seems to be the best Arabic work on the subject.
Al-Nayrizi wrote a book on how to calculate the direction of the sacred holy Ka'bah in Mecca (it was important for Muslims to be able to do this since they had to face that direction five times each day when performing the daily prayer). In this work he effectively uses the tan function, but he was not the first to use these trigonometrical ideas.