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  2. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.

  3. Inverse trigonometric functions - Wikipedia

    en.wikipedia.org/.../Inverse_trigonometric_functions

    The most common convention is to name inverse trigonometric functions using an arc- prefix: arcsin(x), arccos(x), arctan(x), etc. [1] (This convention is used throughout this article.) This notation arises from the following geometric relationships: [ citation needed ] when measuring in radians, an angle of θ radians will correspond to an arc ...

  4. Trigonometric substitution - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_substitution

    Substitutions of hyperbolic functions can also be used to simplify integrals. [ 4 ] For example, to integrate 1 / a 2 + x 2 {\displaystyle 1/{\sqrt {a^{2}+x^{2}}}} , introduce the substitution x = a sinh ⁡ u {\displaystyle x=a\sinh {u}} (and hence d x = a cosh ⁡ u d u {\displaystyle dx=a\cosh u\,du} ), then use the identity cosh 2 ⁡ ( x ...

  5. Inverse hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/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.).

  6. Proofs of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/Proofs_of_trigonometric...

    Trigonometric functions specify the relationships between side lengths and interior angles of a right triangle. For example, the sine of angle θ is defined as being the length of the opposite side divided by the length of the hypotenuse.

  7. Ivy League teams to be eligible for FCS playoffs beginning in ...

    www.aol.com/sports/ivy-league-teams-eligible-fcs...

    Harvard tied with Dartmouth and Columbia atop the conference at 5-2 this season, but scored head-to-head wins over both teams. Officially, the Ivy League recognized all three teams as co-champions.

  8. Top 5 nursing trends shaping health care in 2025 - AOL

    www.aol.com/top-5-nursing-trends-shaping...

    2. Ongoing Nursing Staff Shortages Could Impact Patient Care and Outcomes. Although the shortage of nursing staff isn't technically a new trend, the struggle to fully staff hospitals will continue ...

  9. List of integrals of inverse trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/List_of_integrals_of...

    There are three common notations for inverse trigonometric functions. 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.