**Inverse Trigonometric Functions **ML Aggarwal ISC Class-12 Understanding APC Mathematics Solutions Chapter-2. Step by step Solutions of ML Aggarwal ISC Understanding APC Mathematics Class-12 Exercise 2.1, Exe 2.2 And Exe 2.3 With Chapter Test Questions. Visit official Website **CISCE** for detail information about ISC Board Class-12 Mathematics.

## Inverse Trigonometric Functions M.L. Aggarwal ISC Class-12 ch-2

Class: | 12th |

Subject: | Mathematics |

Chapter : | Ch-2 Inverse Trignometric Functions Page 105-158 |

Board | ISC |

Writer | ML Aggarwal ISC Understanding Vol-I |

Publications | APC Arya Publications |

-: Select Topics :-

### Inverse Trigonometric Functions M.L. Aggarwal ISC Class-12 ch-2

**Inverse Trigonometric Functions:** Trigonometric functions are many-one functions but we know that inverse of function exists if the function is bijective. If we restrict the domain of trigonometric functions, then these functions become objective and the inverse of trigonometric functions are defined within the restricted domain. The inverse of f is denoted by ‘f^{-1}‘.

Let y = f(x) = sin x, then its inverse is x = sin^{-1} y.

**Inverse Trigonometric Functions**

The inverse trigonometric functions are also known as** arc function** as they produce the length of the arc, which is required to obtain that particular value. There are six inverse trigonometric functions which include arcsine (sin^{-1}), arccosine (cos^{-1}), arctangent (tan^{-1}), arcsecant (sec^{-1}), arccosecant (cosec^{-1}), and arccotangent (cot^{-1}).

**Inverse Rational Function**

A rational function is a function of form f(x) = P(x)/Q(x) where Q(x) ≠ 0. To find the inverse of a rational function, follow the following steps. An example is also given below which can help you to understand the concept better.

- Replace f(x) = y
- Interchange x and y
- Solve for y in terms of x
- Replace y with f
^{-1}(x) and the inverse of the function is obtained.

**Inverse Hyperbolic Functions**

Just like inverse trigonometric functions, the inverse hyperbolic functions are the inverses of the hyperbolic functions. There are mainly 6 inverse hyperbolic functions exist which include sinh^{-1}, cosh^{-1}, tanh^{-1}, csch^{-1}, coth^{-1}, and sech^{-1}.

**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^{-1}x 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.

**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.

**Exe-2.1,**

### Inverse Trigonometric Functions ISC Class-12

Page-105, 106

**Exe-2.2,**

Inverse Trigonometric Functions Understanding APC Mathematics ISC Class-12

Page-147, 148, 149

**Exe-2.3**

Inverse Trigonometric Functions Understanding APC Mathematics ISC Class-12

Page-156, 157

**Chapter Test **

### Inverse Trigonometric Functions Understanding APC Mathematics ISC Class-12

Page-158

-: End of **Inverse Trigonometric Function ML **Aggarwal Vol-2 ISC Class-12 Solutions:-

Return to :- ML Aggarwal ISC Class-12 APC Understanding Maths Solutions

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