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Title: Math notes for trigonometry
Description: Mathematics Notes Chapter 2 Inverse Trigonometric Functions.
Description: Mathematics Notes Chapter 2 Inverse Trigonometric Functions.
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Mathematics Notes for Class 12 Chapter 2
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
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, 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
...
Now, y = sin-1(x), y ∈ [π / 2 , π / 2] and x ∈ [-1,1]
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(ii) There is only one value among these values which lies in the interval [π / 2 , π / 2]
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Domain and Range of Inverse Trigonometric FunctionsGraphs of Inverse Trigonometric
Functions
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Properties of Inverse Trigonometric Functions
Property I
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Property II
Property III
Property IV
Property V
Property VI
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Property VII
Property VIII
Property IX
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Property X
Property XI
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Property XII
Important Results
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where Sk denotes the sum of the product of x1,x2,…xn takes k at a time
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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
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(i) Principal Solution – The least value of unknown angle which satisfies the given equation,
is called a principal solution of trigonometric equation
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ncerthelp
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The solution consisting of all possible solutions of a trigonometric equation is called
its general solution
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(ii) Do not cancel common factors involving the unknown angle on LHS and RHS
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(iii) (a) Equation involving sec θ or tan θ can never be a solution of the form (2n + 1) π / 2
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For Class 11
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Title: Math notes for trigonometry
Description: Mathematics Notes Chapter 2 Inverse Trigonometric Functions.
Description: Mathematics Notes Chapter 2 Inverse Trigonometric Functions.