The arcsine function (one of the inverse trigonometric functions) is the sine function y=sinx(x∈[-? π,? π]), expressed as y=arcsinx or siny=x(x∈[- 1, 1]). According to the symmetry of the original function and its inverse function about a three-quadrant bisector, the image of sine function and the image of arcsine function are also symmetrical about a three-quadrant bisector.

In mathematics, the inverse trigonometric function (sometimes called arcus function, inverse function or circular metric function) is the inverse function of trigonometric function (with appropriate restricted domain).

Specifically, they are the inverse functions of sine, cosine, tangent, cotangent, secant and auxiliary functions, and are used to get an angle from the triangle ratio of any angle. Inverse trigonometric functions are widely used in engineering, navigation, physics and geometry.

The meaning of arcsinx:

(1) arcsinx is the angle (radian number) on (principal value area).

(2) The sine value of this angle (radian number) is equal to x, that is, sin (arcsinx) = x. 。

Function image: We know that the image of function y=f(x) and the image of its inverse function y=f- 1(x) are symmetrical about the straight line y = x. First, draw the image of function y=sinx, and draw it with flat glass or transparent paper and turn it over. From the image, we can get the following two conclusions:

(3) The arcsine function y=arcsinx is the increasing function in the interval [- 1, 1];

(4) The image of the arcsine function y=arcsinx is symmetrical about the origin, which means that it is odd function, that is, arcsin(-x)=-arcsinx, x ∈ [- 1, 1].