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CBSE Notes Class 12 Maths Inverse Trigonometric Functions

by aglasem
December 9, 2019
in 12th Class
Reading Time: 11 mins read
0

Class 12 Maths Inverse Trigonometric Functions – Get here the Notes for Class 12 Maths Inverse Trigonometric Functions. Candidates who are ambitious to qualify the Class 12 with good score can check this article for Notes. This is possible only when you have the best CBSE Class 12 Maths study material and a smart preparation plan. To assist you with that, we are here with notes. Hope these notes will helps you understand the important topics and remember the key points for exam point of view. Below we provided the Notes of Class 12 Maths for topic Inverse Trigonometric Functions.

  • Class: 12th
  • Subject: Maths 
  • Topic: Inverse Trigonometric Functions
  • Resource: Notes

CBSE Notes Class 12 Maths Trigonometric Functions

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Candidates who are pursuing in Class 12 are advised to revise the notes from this post. With the help of Notes, candidates can plan their Strategy for particular weaker section of the subject and study hard. So, go ahead and check the Important Notes for Class 12 Maths Inverse Trigonometric Functions

Inverse Function

If y = f(x) and x = g(y) are two functions such that f (g(y)) = y and g (f(y)) = x, then f and y are said to be inverse of each other

i.e., g = f-1

IF y = f(x), then x = f-1(y)

Inverse Trigonometric Functions

If y = sin X-1, then x = sin-1 y, similarly for other trigonometric functions.

This is called inverse trigonometric function .

Now, y = sin-1(x), y ∈ [π / 2 , π / 2] and x ∈ [-1,1].

(i) Thus, sin-1x has infinitely many values for given x ∈ [-1, 1].

(ii) There is only one value among these values which lies in the interval [π / 2 , π / 2]. This value is called the principal value.

Domain and Range of Inverse Trigonometric FunctionsGraphs of Inverse Trigonometric Functions

CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations
CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations
CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations

Properties of Inverse Trigonometric Functions

Property I

CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations
CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations

Property II

CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations

Property III

CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations

Property IV

CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations

Property V

CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations

Property VI

CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations

Property VII

CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations

Property VIII

CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations
CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations

Property IX

CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations

Property X

CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations
CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations

Property XI

CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations

Property XII

CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations
CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations

Important Results

CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations

where Sk denotes the sum of the product of x1,x2,…xn takes k at a time.

Inverse Hyperbolic Functions

If sinh y = x, then y is called the inverse hyperbolic sine of x and it is written as y = sinh-1 x.

Similarly, cosh-1 x, tan h-1 x etc., can be defined,

Domain and Range of Inverse Hyperbolic Functions

CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations

Relation between Inverse Circular Functions and Inverse Hyperbolic Functions

(i) sinh-1x = – i sin-1(ix)

(ii) cosh-1x = – i cos-1 x .

(iii) tanh--1x = – i tan-1(ix)

Important Results

CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations

Trigonometric Equation

An equation involving one or more trigonometrical ratios of unknown angle is called a trigonometric equation .

Solution/Roots of a Trigonometric Equation

A value of the unknown angle which satisfies the given equation, is called a solution or root of the equation.

The trigonometric equation may have infinite number of solutions.

(i) Principal Solution – The least value of unknown angle which satisfies the given equation, is called a principal solution of trigonometric equation.

(ii) General Solution – We know that, trigonometric function are periodic and solution of trigonometric equations can be generalised with the help of the periodicity of the trigonometric functions. The solution consisting of all possible solutions of a trigonometric equation is called its general solution.

Important Results

CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations
CBSE Class 11 and 12 Maths Notes Inverse T - Functions and T - Equations

Important Points to be Remembered

(i) While solving an equation, we have to square it, sometimes the resulting roots does not satisfy the original equation.

(ii) Do not cancel common factors involving the unknown angle on LHS and RHS.Because it may be the solution of given equation.

(iii) (a) Equation involving sec θ or tan θ can never be a solution of the form (2n + 1) π / 2.

(b) Equation involving coseca or cote can never be a solution of the form θ = nπ.
For Class 11

Class 12 Key Points, Important Questions & Practice Papers

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Hope these notes helped you in your schools exam preparation. Candidates can also check out the Key Points, Important Questions & Practice Papers for various Subjects for Class 12 in both Hindi and English language form the link below.

Class 12 Physics कक्षा 12 व्यावसायिक अध्ययन
Class 12 Chemistryकक्षा 12 समाज शास्त्र
Class 12 Maths कक्षा 12 अर्थशास्त्र
Class 12 Biology कक्षा 12 भूगोल
Class 12 Business Studies
Class 12 Economics
Class 12 Sociology

Class 12 NCERT Solutions

Candidates who are studying in Class 12 can also check Class 12 NCERT Solutions from here. This will help the candidates to know the solutions for all subjects covered in Class 12th. Candidates can click on the subject wise link to get the same. Class 12 Chapter-wise, detailed solutions to the questions of the NCERT textbooks are provided with the objective of helping students compare their answers with the sample answers.

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Class 12 Mock Test / Practice

Mock test are the practice test or you can say the blue print of the main exam. Before appearing in the main examination, candidates must try mock test as it helps the students learn from their mistakes. With the help of Class 12 Mock Test / Practice, candidates can also get an idea about the pattern and marking scheme of that examination. For the sake of the candidates we are providing Class 12 Mock Test / Practice links below.

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Class 12 Exemplar Questions

Exemplar Questions Class 12 is a very important resource for students preparing for the Examination. Here we have provided Exemplar Problems Solutions along with NCERT Exemplar Problems Class 12. Question from very important topics is covered by Exemplar Questions for Class 12.

Physicsगणित
Chemistryभौतिक विज्ञान
Mathsसायन विज्ञान
Biology

Class 12 Maths Chemistry Notes Physics Notes Biology Notes

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