If the two angles are complementary, then sinα=cosβ and cosα=sinβ. If the two angular gyrus are complementary, then sinα=sinβ and cosα=-cosβ. On the same plane, if the sum of two non-overlapping angles with the same vertex angle is equal to 180 degrees, then we say that these two angles are complementary (mutually complementary). If the sum of two angles is 90, they are called "complementary angles" or simply "complementary angles".

Brief introduction of trigonometric function

Trigonometric function is one of the basic elementary functions, which takes the angle (the most commonly used radian system in mathematics, the same below) as the independent variable, and the angle corresponds to the coordinates where the terminal edge of any angle intersects with the unit circle or its ratio as the dependent variable. It 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 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.