Trigonometric function theorem is one of the basic elementary functions, which takes the most commonly used radian system angles in mathematics as independent variables, and the angle corresponds to the coordinates where the terminal edge of any angle intersects with the unit circle or its ratio as dependent variables. It can also be defined by 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 the solution of infinite series or specific differential equation, allowing its value to be extended to any real value or even complex value. Common trigonometric functions are sine function, cosine function and tangent function.

The content of trigonometric function

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, which is very important in many applications such as studying triangles and modeling periodic phenomena. 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.