Table of Contents
Domain and Range of Inverse Trigonometric Formulas
Domain: The domain of the inverse trigonometric function is the set of all real numbers.
Range: The range of the inverse trigonometric function is the set of all real numbers.
The Formula of Inverse Trigonometric Functions
The inverse trigonometric functions are the inverse of the trigonometric functions. The inverse trigonometric functions are:
sin-1(x)
cos-1(x)
tan-1(x)
cot-1(x)
sec-1(x)
csc-1(x)
Graph of Inverse Trigonometric Function
The graph of inverse trigonometric function is a curve that shows the inverse relationship between the angle of incidence and the angle of reflection. It starts from the point (0, 1) and goes up to the point (1, 0).
1 – Arcsine Function
The arcsine function, or inverse sine function, is a mathematical function that takes a real number and returns the angle in radians that is the sine of that number.
2 – Arccosine Function
The arccosine function is a mathematical function that calculates the angle of a point on a unit circle from the x-coordinate. It is written as arccos(x) or arc cosine(x), and it returns a value in radians. The arccosine function is also known as the inverse cosine function.
3 – Arctangent Function
The arctangent function is a real-valued function that takes a real number as input and outputs the arctangent of that number. The arctangent function is defined as:
arctangent(x) = atan(x)
4 – Arccotangent Function
The arccotangent function is a function that takes in a real number and outputs the arc cotangent of that number. The arc cotangent of a number is the inverse of the cotangent function, so it calculates the angle of a cotangent line from 0 to pi radians.
5 – Arcsecant Function
The arcsecant function is the inverse of the secant function. It calculates the angle between two points on a unit circle, given the x- and y-coordinates of those points.
6 – Arccosecant Function
The arccosecant function is the inverse of the arccosine function. It is used to find angles in radians that are in the range of – π/2 to π/2.
The arccosecant function is written as arccosec(x) and it takes the value of x as its input.
