Arabic mathematics, also known as Islamic mathematics, made great progress in the Middle Ages. Mathematicians in this period made contributions to algebra, geometry, number theory and trigonometry. However, when we deeply understand the research contents of this period, we can find that Arab mathematicians did not systematically study trigonometric functions.

Algebra is the obvious strength of Arabic mathematics. They developed the basic theory of algebra and solved many algebraic equations. In addition, in geometry, they studied the nature of graphics and the calculation method of area and volume. Number theory is also their research focus, involving prime numbers, divisibility and indefinite equations.

However, although Arab mathematicians know and use some knowledge and skills related to trigonometric functions, such as using sine and cosine to solve some geometric and astronomical problems, they have not systematically defined, classified and studied trigonometric functions like modern mathematics.

The systematic research direction of trigonometric function;

The systematic study of trigonometric function began with ancient Greek mathematicians, who made a preliminary discussion on the application and properties of trigonometric function. The in-depth study and systematic understanding of trigonometric functions were mainly completed during the European Renaissance.

During the Renaissance, trigonometric function became an important tool to solve various problems due to the development of astronomy, physics and engineering. In order to meet the needs of practical application, European mathematicians began to study trigonometric functions in depth and established a complete theoretical system.

Among them, the most important achievement is Vieta's book Trigonometry. In this book, David elaborated the definition, properties and related formulas of trigonometric function. He introduced modern trigonometric function symbols and gave series expansions of sine, cosine and tangent functions, which provided a basis for the calculation and application of trigonometric functions.

David also found many theorems and formulas related to trigonometric functions, such as sine theorem, cosine theorem and tangent sum difference formula. These theorems and formulas provide important tools for solving various practical problems and become an important part of trigonometric function system.