The content includes-trigonometric function? Plane vector? Trigonometric identity transformation

As an important concept in modern mathematical physics, vector was first used by British mathematician Hamilton. Although the term vector comes from Hamilton, the idea of vector as a directed line segment has a long history.

There are three main lines in the origin and development of vector theory: parallelogram law of velocity and force in physics, position geometry and geometric representation of complex numbers.

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 any positive and negative values, even complex values.

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Modern vector theory is based on the geometric representation of complex numbers. /kloc-in the 0/8th century, due to the use of complex numbers in some mathematical derivation, the geometric representation of complex numbers has become a hot topic. Hamilton discovered quaternions in the process of making a modular simulator of three-dimensional complex numbers. Subsequently, Gibbs and Harvey created a vector analysis system based on quaternion, which was finally widely accepted.

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, 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.

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