In mathematics, the inverse trigonometric functions (occasionally called cyclometric functions) are the inverse functions of the trigonometric functions with suitably restricted domains.
The notations sin−1, cos−1, tan−1, etc. are often used for arcsin, arccos, arctan, etc., but this convention logically conflicts with the common semantics for expressions like sin2(x), which refer to numeric power rather than function composition, and therefore may result in confusion between multiplicative inverse and compositional inverse.
In computer programming languages the functions arcsin, arccos, arctan, are usually called asin, acos, atan. Many programming languages also provide the two-argument atan2 function, which computes the arctangent of y / x given y and x, but with a range of (−π, π].
Read more about Inverse Trigonometric Functions: Etymology of The Arc- Prefix, Principal Values, Relationships Among The Inverse Trigonometric Functions, Relationships Between Trigonometric Functions and Inverse Trigonometric Functions, General Solutions, Derivatives of Inverse Trigonometric Functions, Expression As Definite Integrals, Infinite Series, Continued Fractions For Arctangent, Indefinite Integrals of Inverse Trigonometric Functions, Two-argument Variant of Arctangent, Arctangent Function With Location Parameter, Logarithmic Forms, Arctangent Addition Formula, Application: Finding The Angle of A Right Triangle, Practical Considerations
Other articles related to "trigonometric functions, trigonometric, trigonometric function, inverse trigonometric functions":
... The computation of trigonometric functions is a complicated subject, which can today be avoided by most people because of the widespread availability of computers and scientific ... describes details of their computation in three important contexts the historical use of trigonometric tables, the modern techniques used by computers, and a few "important" angles ... The first step in computing any trigonometric function is range reduction—reducing the given angle to a "reduced angle" inside a small range of angles, say 0 to π/2 ...
... be used to evaluate integrals involving trigonometric functions ... Using Euler's formula, any trigonometric function may be written in terms of eix and e−ix, and then integrated ... is often simpler and faster than using trigonometric identities or integration by parts, and is sufficiently powerful to integrate any rational expression involving trigonometric functions ...
... For integrals and derivatives of trigonometric functions, see the relevant sections of Differentiation of trigonometric functions, Lists of integrals and List of integrals of ... Below is the list of the derivatives and integrals of the six basic trigonometric functions ...
... The notation is the one used in Arabic notation for the inverse functions like. ...
... more integrals List of integrals of inverse trigonometric functions. ...
Famous quotes containing the words functions and/or inverse:
“When Western people train the mind, the focus is generally on the left hemisphere of the cortex, which is the portion of the brain that is concerned with words and numbers. We enhance the logical, bounded, linear functions of the mind. In the East, exercises of this sort are for the purpose of getting in tune with the unconscious—to get rid of boundaries, not to create them.”
—Edward T. Hall (b. 1914)
“Yet time and space are but inverse measures of the force of the soul. The spirit sports with time.”
—Ralph Waldo Emerson (1803–1882)