NCERT Solutions Class 12 Maths Chapter 2 Inverse Trigonometric Functions

The inverse trigonometric functions help to determine the angle values for the given trigonometric ratios. These functions commonly include sin^-1 x, cos^-1 x, tan^-1 x, cot^-1 x, cosec^-1 x, sec^-1 x. There are various formulas that relate these inverse trigonometric functions.

It is very important to learn and practice all these formulas so as to understand their applications by solving the sums given in the practice exercises of NCERT Class 12 Maths Chapter 2 Inverse Trigonometric Functions.

You can get one of the most relevant NCERT Solutions for Chapter 2 Maths Class 12 Inverse Trigonometric Functions on Vedantu. These NCERT Solutions are among the top-rated study resources for the Class 12 topic of Inverse Trigonometric Functions. You can download the PDF comprising these solutions for free. Also, NCERT Solutions for this chapter are available on our mobile application. These solutions are prepared by the subject matter experts at Vedantu in strict adherence to the NCERT guidelines for Class 12. So, students can rely on these NCERT solutions for Class 12 Maths Chapter 2 for their exam preparation.

Yes, you can refer to the NCERT Solutions for Chapter 2 Maths Class 12 Inverse Trigonometric Functions for your IIT JEE preparation as well. These NCERT solutions are worked out in a step by step method that helps students to understand the logical analysis of every sum of Inverse Trigonometric Functions. When students develop a deeper understanding of the problem-solving techniques for every type of sum covered in this chapter, only then they can solve these sums much faster during their IIT JEE examination.

Although the domain of inverse trigonometric functions varies depending on the particular function, they typically have narrow domains to guarantee one-to-one correspondence.

For Example, sin^-1(x) has a domain of [-1, 1] and its range is [−π/2,π/2].

We restrict inverse trigonometric functions to make sure they give us only one answer for each input number. The functions wouldn't function correctly without these limitations/restrictions since they wouldn't be "one-to-one," which means that there would be several possible output values for each input integer. By limiting or restricting the input numbers(domain) and output responses(range), we ensure that each input has a unique outcome, which makes functions easier to understand and use.

Restricted Domain: Inverse trigonometric functions have restricted domains to ensure they are one-to-one functions. This indicates that there is only one output value that corresponds to each input value.

Principal Value Ranges: The primary range of values for each inverse trigonometric function indicates the range of probable solutions it can provide. These value sets are carefully chosen to provide consistency

The limits of inverse trigonometric functions depend on which specific function you're considering and the direction (positive or negative infinity) from which you're approaching the limit.

For Tangent:

• lim (as x approaches positive infinity) of arctan(x) = π/2

• lim (as x approaches negative infinity) of arctan(x) = -π/2

For Sine:

• lim(as x approaches positive infinity) of arcsin(x)=π/2

• lim(as x approaches negative infinity) of arcsin(x)=-π/2

For Cosine:

• lim(as x approaches positive infinity) of arccos(x)=0

• lim(as x approaches negative infinity) of arcsin(x)=π

Here are some real time examples of inverse functions:

• As the speed of the car increases the time taken to cover a certain distance decreases.

• More buses on the road means less space on the road.

• The number of people doing something and the time it takes to do it. As the number of people increases, the time it takes to finish decreases.