NCERT Solutions Exercise 2.1: Inverse Trigonometric Functions

NCERT Solutions Class 12 Maths Chapter 2 - Inverse Trigonometric Functions

``` Page 1

Class XII  Chapter 2 – Inverse Trigonometric Functions Maths
Page 1 of 38

Exercise 2.1
Question 1:
Find the principal value of
Let sin
-1
Then sin y =
We know that the range of the principal value branch of sin
-1
is
and sin
Therefore, the principal value of
Question 2:
Find the principal value of
We know that the range of the principal value branch of cos
-1
is
.
Therefore, the principal value of .
Question 3:
Find the principal value of cosec
-1
(2)
www.ncrtsolutions.blogspot.com
Page 2

Class XII  Chapter 2 – Inverse Trigonometric Functions Maths
Page 1 of 38

Exercise 2.1
Question 1:
Find the principal value of
Let sin
-1
Then sin y =
We know that the range of the principal value branch of sin
-1
is
and sin
Therefore, the principal value of
Question 2:
Find the principal value of
We know that the range of the principal value branch of cos
-1
is
.
Therefore, the principal value of .
Question 3:
Find the principal value of cosec
-1
(2)
www.ncrtsolutions.blogspot.com
Class XII  Chapter 2 – Inverse Trigonometric Functions Maths
Page 2 of 38

Let cosec
-1
(2) = y. Then,
We know that the range of the principal value branch of cosec
-1
is
Therefore, the principal value of
Question 4:
Find the principal value of
We know that the range of the principal value branch of tan
-1
is
Therefore, the principal value of
Question 5:
Find the principal value of
We know that the range of the principal value branch of cos
-1
is
Therefore, the principal value of
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Mathematics (Maths) for JEE Main & Advanced

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FAQs on NCERT Solutions Class 12 Maths Chapter 2 - Inverse Trigonometric Functions

 1. What are inverse trigonometric functions?
Ans. Inverse trigonometric functions are mathematical functions that help find the angle or angles when the trigonometric ratio is known. They are the inverse operations of trigonometric functions and are denoted by sin^(-1), cos^(-1), tan^(-1), etc.
 2. How do inverse trigonometric functions work?
Ans. Inverse trigonometric functions work by taking the ratio of a side length in a right triangle to its hypotenuse and determining the corresponding angle. They help in finding the angle when the trigonometric ratio is given, making them useful in solving various mathematical problems.
 3. What are the ranges and domains of inverse trigonometric functions?
Ans. The ranges and domains of inverse trigonometric functions depend on the specific function. For example, the domain of sin^(-1)(x) is [-1, 1], and the range is [-π/2, π/2]. Similarly, the domain of cos^(-1)(x) is [-1, 1], and the range is [0, π].
 4. How are inverse trigonometric functions used in real-life applications?
Ans. Inverse trigonometric functions have numerous real-life applications. They are used in fields such as engineering, physics, and navigation to solve problems involving angles and distances. For example, they can be used to calculate the angle of elevation or depression in surveying or to determine the distance between two points using triangulation.
 5. What are some important properties of inverse trigonometric functions?
Ans. Some important properties of inverse trigonometric functions include their restricted domains and ranges, their periodicity, and their relationships with trigonometric functions. These properties are essential in understanding and applying inverse trigonometric functions in various mathematical contexts.

Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

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