Inverse Trigonometric Functions:Class 12 Maths NCERT Chapter 2

Key Features of NCERT Material for Class 12 Maths Chapter 2 – Inverse Trigonometric Functions

In this Chapter 2:Inverse trigonometric functions we will see basic concepts of inverse trigonometric functions.In the previous Chapter 1:Relations and functions we have learned about relations and functions, types of relation, types of functions

Quick revision notes

Inverse Trigonometric Functions:Trigonometric functions are many-one functions yet we realize that the inverse of a function exists if the function is bijective. In the event that we confine the domain of trigonometric functions, at that point these functions become bijective and the inverse of trigonometric functions are characterized inside the limited domain. The inverse of f is signified by ‘f-1’. 

Let y = f(x) = sin x, at that point its inverse is x = sin-1 y. 

Domain and Range of Inverse Trigonometric Functions

sin-1(sinθ) = θ; ∀ θ ∈

cos-1(cosθ) = θ; ∀ θ ∈ [0, π]

tan-1(tanθ) = θ; ∀ θ

cosec-1(cosecθ) = 0; ∀ θ ∈ , θ ≠ 0

sec-1(secθ) = θ; ∀ θ ∈ [0, π], θ ≠

cot-1(cotθ) = θ; ∀ θ ∈ (0, π)

sin(sin-1 x) = x, ∀ x ∈ [-1, 1]

cos(cos-1 x) = x; ∀ x ∈ [-1, 1]

tan(tan-1x) = x, ∀ x ∈ R

cosec(cosec-1x) = x, ∀ x ∈ (-∞, -1] ∪ [1, ∞)

sec(sec-1 x) = x, ∀ x ∈ (-∞, -1] ∪ [1, ∞)

cot(cot-1 x) = x, ∀ x ∈ R

Note: sin-1(sinθ) = θ ; sin-1 x should not be confused with (sinx)-1 =1/sinx  or sin-1 x = sin-1(1/x) land correspondingly for other trigonometric functions. 

The estimation of this function, which lies in the range of the chief worth branch, is known as the chief estimation of the inverse trigonometric function. 

Note: Whenever no part of this is referenced, it implies we need to consider the chief worth part of that function

Properties of Inverse Trigonometric Functions

Following substitutions are used to write in simplest form:

Remember Points

(I) Sometimes, it might occur that a portion of the estimations of x that we discover doesn’t fulfill the given condition. 

(ii) While comprehending a condition, don’t drop the basic elements from the two sides.