Inverse Trigonometric Functions: Properties of Inverse Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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What is Inverse Trigonometric Function?

Considering the Domain and Range of the Inverse Functions, Following Formulas Are Important to Be Noted:

  • The inverse trigonometric functions are an important aspect of trigonometric functions, included in the syllabus for class students.
  • In mathematics, the inverse trigonometric functions are the inverse functions of the trigonometric functions.
  • Inverses of trigonometric functions exist solely due to the restrictions existing on the domains and their respective ranges.
  • Being able to solve inverse trigonometric function problems starts by understanding the trigonometric ratios first.
  • Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the angle՚s trigonometric ratios
  • The behavior of these trigonometric functions is usually represented in the form of graphical methods.
  • They play an essential role in calculus as they help to define different integrals.
  • Major applications of inverse trigonometric functions in everyday life are in the fields of science and engineering.

Properties of Inverse Trigonometric Functions

  • The properties of Inverse Trigonometric Functions help to prove a distinct relationship between the different trigonometric entities such as , and .
  • There are a few inverse trigonometric functions properties which are crucial to not only solve problems but also to have a deeper understanding of this concept.
  • The domain of a function is defined as the set of every possible independent variable where the function exists. Inverse Trigonometric Functions are defined in a certain interval.
  • The results obtained with the help of these properties are valid within the principal branches of the inverse trigonometric functions.
  • To recall, inverse trigonometric functions are also called “Arc Functions.” For a given value of a trigonometric function; they produce the length of arc needed to obtain that value.
  • These properties are valid for some values of , where these inverse trigonometric functions are defined with.
  • The range of an inverse function is defined as the range of values of the inverse function that can attain with the defined domain of the function.

Property Set 1

Property Set 2

Derivatives of Inverse Trigonometric Functions