Trigonometric function is a common function about angle in mathematics. In other words, a function with angle as the independent variable and the ratio of angle to any two sides as the dependent variable is called trigonometric function, which relates the inner angle of a right triangle to the ratio of the lengths of its two sides, and can also be equivalently defined as the lengths of various line segments related to the unit circle. Trigonometric function plays an important role in studying the properties of geometric shapes such as triangles and circles, and is also a basic mathematical tool for studying periodic phenomena. In mathematical analysis, trigonometric function is also defined as infinite limit or the solution of a specific differential equation, which allows its value to be extended to any real value or even complex value.

Common trigonometric functions are sine function, cosine function and tangent function. Other trigonometric functions, such as cotangent function, secant function, cotangent function, dyadic function, cofactor function, semidyadic function and semifactorial function, are also used in other disciplines, such as navigation, surveying and engineering. The relationship between different trigonometric functions can be obtained by geometric intuition or calculation, which is called trigonometric identity.

Trigonometric functions are generally used to calculate the sides and angles of triangles with unknown lengths, and are widely used in navigation, engineering and physics. In addition, taking trigonometric functions as templates, we can define a class of similar functions, which are called hyperbolic functions. Common hyperbolic functions are also called hyperbolic sine functions, hyperbolic cosine function and so on. Trigonometric function (also called circular function) is a function of angle; They are very important in studying triangles, simulating periodic phenomena and many other applications. Trigonometric function is usually defined as the ratio of two sides of a right triangle containing this angle, and it can also be equivalently defined as the lengths of various line segments on the unit circle. More modern definitions express them as infinite series or solutions of specific differential equations, allowing them to be extended to arbitrary positive and negative values, even complex values.