Find the domain of inverse trigonometric functions?

The domain of inverse trigonometric functions refers to the set of input values (or the range of values) for which the inverse trigonometric functions are defined.

Here are the domains for the inverse trigonometric functions:

Inverse Sine Function (sin⁻¹(x)):

The domain is: [-1, 1]
This means that the inverse sine function is only defined for values of x between -1 and 1, inclusive.
Inverse Cosine Function (cos⁻¹(x)):

The domain is: [-1, 1]
The inverse cosine function is also only defined for values of x between -1 and 1, inclusive.
Inverse Tangent Function (tan⁻¹(x)):

The domain is: (-∞, ∞)
The inverse tangent function is defined for all real numbers, so its domain is the entire set of real numbers.
Inverse Cotangent Function (cot⁻¹(x)):

The domain is: (-∞, ∞)
Like the inverse tangent function, the inverse cotangent function is also defined for all real numbers.
Inverse Secant Function (sec⁻¹(x)):

The domain is: (-∞, -1] ∪ [1, ∞)
The inverse secant function is defined for values of x less than or equal to -1 or greater than or equal to 1.
Inverse Cosecant Function (csc⁻¹(x)):

The domain is: (-∞, -1] ∪ [1, ∞)
The inverse cosecant function is defined for values of x less than or equal to -1 or greater than or equal to 1.
Summary of the domains:
sin⁻¹(x) and cos⁻¹(x): [-1, 1]
tan⁻¹(x) and cot⁻¹(x): (-∞, ∞)
sec⁻¹(x) and csc⁻¹(x): (-∞, -1] ∪ [1, ∞)