Trigonometric function is a transcendental function in elementary functions in mathematics. Their essence is the mapping between any set of angles and a set of ratio variables. The usual trigonometric function is defined in a plane rectangular coordinate system.
Its definition field is the whole real number field. The other is defined in a right triangle, but it is incomplete. Modern mathematics describes them as the limit of infinite sequence and the solution of differential equation, and extends their definitions to complex system.
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 is called trigonometric identity.
Inverse function of trigonometric function:
The inverse function of trigonometric function is a multivalued function. They are arcsine x, anti-cosine anti-cosine x, anti-tangent anti-tangent x, anti-tangent anti-tangent x and so on. , which respectively represent sine angle, cosine angle, tangent angle, cotangent angle, secant angle and cotangent angle.
In order to define the inverse trigonometric function as a single-valued function, the value y of the arcsine function is defined as y=-π/2≤y≤π/2, and y is the principal value of the arcsine function, denoted as y = arcsinx. Accordingly, the principal value of the inverse cosine function y=arccos x is limited to 0 ≤ y ≤π; The principal value of arctangent function y=arctan x is limited to -π/2.
In fact, the inverse trigonometric function can't be called a function, because it doesn't meet the requirement that the independent variable corresponds to the function value. Its image and its original function are symmetrical about the function y = X, and its concept was first put forward by Euler. The inverse trigonometric function was first expressed in the form of arc+function name, instead of f- 1(x).
There are three main inverse trigonometric functions:
Y=arcsin(x), domain [- 1, 1], range [-π/2, π/2], and red line is used for images.
Y=arccos(x), domain [- 1, 1], range [0, π], and blue line is used for image.
Y=arctan(x), domain (-∞, +∞), range (-π/2, π/2), and the image is drawn with a green line.