Nov. 12, 2019

Introduction & Definition of Inverse Trigonometric Function,Domain & Range of Inverse Trigonometric Function:

Inverse Mapping of A Mapping

If f is a mapping from a set A to a set B, then the set A is called the domain and the set B is called the co-domain of the mapping f. 

Let f : A → B be bijective i.e., both one-to-one and onto. Then the mapping g : B → A is called the inverse mapping of the mapping f if 

f (x) = y 

g(y) = x where, xA , yB

The inverse mapping of the mappinf f is usually represented by f-1.

Only one-to-one onto mappings posses inverse mapping. 

From the defition of inverse mapping it is obvious that if f(x) = y, then f-1(y) = x, and vice-versa. 

Inverse Circular Functions and Their Principle and General Values 

Inverse circular functions are defined as follows: 

If sin θ=x, then or arc sin x.

If cos θ=x, then or arc cos x,

If tan θ=x, then or arc tan x, 

and similar definitions for other trigonometric functions. 

Thus if then sin-1 x represents an angle whose sine is x.