The most important contributor in trigonometry is Pythagoras.
We'll recall the Pythagorean theorem that states the following:In a right angle triangle, the square of the length of hypotenuse is equal to the sum of the squares of the lengths of the legs of triangle.
a^2 = b^2 + c^2
In trigonometry, Pythagorean theorem helps in finding Pythagorean identity, in the trigonometric circle, whose radius is the unit:
(sin x)^2 + (cos x)^2 = 1
But Pythagoras' contributions were not attributed to trigonometry, only, but to mathematical field, in general.
Another important contributor was Nicholas (Nicolaus) Copernicus, whose scale model of the Solar System, was known as being the first one.
Therefore, your list can begin with the names of these two important contributors: Pythagoras, Nicholas Copernicus.