# Islam and Maths:Trigonometry and Geometry.

Trigonometry and Geometry

Trigonometry flourished in Islamic civilizations and became a stand alone discipline, as humans had used trigonometry mostly in relation to astronomy. Indeed, Nasir al-Din aTusi, a mathematician of the 13th century, is credited with establishing trigonometry as an independent field. Below, we take the reader to a (or the) principle discovery and element in trigonometry: the sine law.

3.1 The Plane and Spherical Sine Laws

The plane sine law states that, for any 2-D triangle, we have:

b sin (3) a sin(a) C sin(y)’

where a, b, and c are the sides of the triangle, and a, 3, and y are the opposite angles of the sides, respectively. In laymen terms, the sine law stipulates that the ratio of a side to the opposite angle is equivalent to a ratio of another side and it’s opposite angle. See the below diagram to help illustrate the equation better.

α b a

Figure 1: Plane Triangle. Source:

Now, the spherical sine law is as follows:

sin(a) sin (A) sin (3) sin (B) sin(7) sin(C)

Note that the above holds for a unit sphere, or a sphere with radius 1, and that the triangle is actually curved onto the sphere, instead of on a plane. See the diagram on the next page for an illustration.