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
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
Properties of Inverse Trigonometric Functions
Property I
Property II
Property III
Property IV
Property V
Property VI
Property VII
Property VIII
Property IX
Property X
Property XI
Property XII
Important Results
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
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
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
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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Class 12 NCERT Solutions
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Class 12 Mock Test / Practice
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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.
