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For arcsine, the series can be derived by expanding its derivative, , as a binomial series, and integrating term by term (using the integral definition as above). The series for arctangent can similarly be derived by expanding its derivative 1 1 + z 2 {\textstyle {\frac {1}{1+z^{2}}}} in a geometric series , and applying the integral definition ...
The arcsine function, for instance, could be written as sin −1, asin, or, as is used on this page, arcsin. For each inverse trigonometric integration formula below there is a corresponding formula in the list of integrals of inverse hyperbolic functions .
A ray through the unit hyperbola = in the point (,), where is twice the area between the ray, the hyperbola, and the -axis. The earliest and most widely adopted symbols use the prefix arc-(that is: arcsinh, arccosh, arctanh, arcsech, arccsch, arccoth), by analogy with the inverse circular functions (arcsin, etc.).
In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined.
The arcsine distribution appears in the Lévy arcsine law, in the Erdős arcsine law, and as the Jeffreys prior for the probability of success of a Bernoulli trial. [ 1 ] [ 2 ] The arcsine probability density is a distribution that appears in several random-walk fundamental theorems.
From Wikipedia, the free encyclopedia. Redirect page. Redirect to: Inverse trigonometric functions
However, the Arcsine Integral does have some elementary function values. These values can be determined by integrating the derivative of the arcsine integral, which is the quotient of the Arcsine divided by the Identity Function - the Cardinalized Arcsine. The Arcsine Integral is exactly the original antiderivative of the Cardinalized Arcsine.
From an avoided double redirect: This is a redirect from an alternative title or related topic of Arcsine, another redirect to the same title. Because double redirects are disallowed, both pages currently point to Inverse trigonometric functions .