## Inverse Trigonometric Functions Formula for CBSE Class 12 Maths - Free PDF Download

## FAQs on CBSE Class 12 Maths Chapter-2 Inverse Trigonometric Functions Formula

1. What is meant by Inverse Trigonometric Function?

The inverse trigonometric functions are called anti trigonometric functions or sometimes known as the cyclometric functions or arcus functions. The inverse trigonometric functions of sine, cosine, tangent, secant, cosecant, and cotangent are used to determine the angle of a triangle from any of the trigonometric functions.

2. What are the applications of Inverse Trigonometric Function?

It is widely used in different fields including geometry, physics, engineering etc. But in general, the convention symbol to indicate the inverse trigonometric function with the help of arc-prefix such as arcsin(x), arccos(x), arctan(x), arccsc(x), arcsec(x), arccot(x). In order to identify the sides of a triangle when the remaining side lengths are known.

Take into the function y = f(x), and x = g(y) then the inverse function is expressed as g = f^{-1},

This implies that if y=f(x), then x = f^{-1}(y).

In a way that f(g(y))=y and g(f(y))=x.

Example of Inverse trigonometric functions: x= sin^{-1}y

3. What are the properties of inverse trigonometric functions?

Below is the inverse trigonometric function formula:

sin

^{-1}(1/a) = cosec^{-1}(a), a ≥ 1 or a ≤ – 1sin

^{-1}(–a) = – sin^{-1}(a), a ∈ [– 1, 1]cos

^{-1}(1/a) = sec^{-1}(a), a ≥ 1 or a ≤ – 1cos

^{-1}(–a) = π – cos^{-1}(a), a ∈ [– 1, 1]tan

^{-1}(1/a) = cot^{-1}(a), a>0tan

^{-1}(–a) = – tan^{-1}(a), a ∈ Rsec

^{-1}(–a) = π – sec^{-1}(a), | a | ≥ 1cosec

^{-1}(–a) = –cosec^{-1}(a), | a | ≥ 1cot

^{-1}(–a) = π – cot^{-1}(a), a ∈ R