 He listed the six distinct cases of a right-angled triangle in spherical trigonometry, and in his "On the Sector Figure", he stated the law of sines for plane and spherical triangles, discovered the law of tangents for spherical triangles, and provided proofs for both these laws.Nasir al-Din al-Tusi has been described as the creator of trigonometry as a mathematical discipline in its own right.In the 15th century, Jamshīd al-Kāshī provided the first explicit statement of the law of cosines in a form suitable for triangulation.