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The following table shows how inverse trigonometric functions may be used to solve equalities involving the six standard trigonometric functions. It is assumed that the given values θ , {\displaystyle \theta ,} r , {\displaystyle r,} s , {\displaystyle s,} x , {\displaystyle x,} and y {\displaystyle y} all lie within appropriate ranges so that ...
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.
For example, the inverse of a cubic function with a local maximum and a local minimum has three branches (see the adjacent picture). The arcsine is a partial inverse of the sine function. These considerations are particularly important for defining the inverses of trigonometric functions. For example, the sine function is not one-to-one, since
Pages in category "Inverse trigonometric functions" The following 47 pages are in this category, out of 47 total. This list may not reflect recent changes. ...
Differentiation of trigonometric functions; Exact trigonometric constants; History of trigonometry; Inverse trigonometric functions; Law of cosines; Law of cotangents; Law of sines; Law of tangents; List of integrals of inverse trigonometric functions; List of integrals of trigonometric functions; List of trigonometric identities; Mollweide's ...
The table below displays names and domains of the inverse trigonometric functions along with the range of their usual principal values in radians. Name Symbol
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