I. Introduction of Inverse Trigonometric Function
Inverse trigonometric function is a basic elementary function. It is the floorboard of the functions of arcsinx, arccosx, arctanx, arccotx, arcsecx and arccscx, representing the angle of X respectively.
Second, the definition of function
Function was originally translated by Li, a mathematician of Qing Dynasty in China, in his book Algebra. He translated this way because "whoever believes in this variable is the function of that variable", that is, the function means that one quantity changes with another quantity, or that one quantity contains another quantity.
Classification of inverse trigonometric functions;
1, arcsine function
The inverse function of sine function y = sinx on [-π/2, π/2] is called arcsine function. Arcsinx represents an angle with a sine value of x, and the value range of the angle is within the range of [-π/2, π/2]. Domain [- 1, 1], range [-π/2, π/2].
2. Anti-cosine function
The inverse function of cosine function y = cosx on [0, π] is called anti-cosine function. Recorded as arccosx, it represents the angle whose cosine value is x, and the range of the angle is within the range of [0, π]. Definition domain [- 1, 1] and value domain [0, π].
3. Arctangent function
The inverse function of the tangent function y = tanx on (-π/2, π/2) is called the arc tangent function. Recorded as arctanx, it represents the angle with the tangent value of x, and the value range of the angle is within the range of (-π/2, π/2). The field r, range (-π/2, π/2).
4. Inverse cotangent function
The inverse function of cotangent function y = cotx on (0, π) is called inverse cotangent function. Recorded as arccotx, it represents the angle with cotangent value of x, and the value range of the angle is within the range of (0, π). Definition domain r, value domain (0, π).
5. Arctangent function
The inverse function of secx = secx on [0, π/2] u (π/2, π) is called arc tangent function. Arcsecx, which represents the angle with secant value of x, is in the range of [0, π/2] u (π/2, π). The definition domain (-∞,-1)u[ 1, +∞) and the value domain [0, π/2] u (π/2, π).
6. Inverse cotangent function
The inverse function of cotangent function y = cscx on [-π/2,0 0) u (0 0,π/2] is called the inverse cotangent function. Arccscx represents an angle whose cotangent value is x, and the range of the angle is [-π/2,0 0) u (0 0,π/2]. The definition domain (-∞,-1)u[ 1, +∞) and the value domain [-π/2,0 0] u (0 0,π/2].