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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.
The trigonometric functions are periodic, and hence not injective, so strictly speaking, they do not have an inverse function. However, on each interval on which a trigonometric function is monotonic, one can define an inverse function, and this defines inverse trigonometric functions as multivalued functions.
Many slide rules – especially "trig" and higher models – include an "ST" (sines and tangents) or "SRT" (sines, radians, and tangents) scale on the front or back of the slide, for computing with trigonometric functions of angles smaller than about 0.1 radian (or within about 0.1 radian of /, that is, within 5.7 degrees of 90 degrees, in the ...
To avoid any confusion, an inverse trigonometric function is often indicated by the prefix "arc" (for Latin arcus). [9] [10] For instance, the inverse of the sine function is typically called the arcsine function, written as arcsin(x). [9] [10] Similarly, the inverse of a hyperbolic function is indicated by the prefix "ar" (for Latin ārea). [10]
Graphs of the inverse hyperbolic functions The hyperbolic functions sinh, cosh, and tanh with respect to a unit hyperbola are analogous to circular functions sin, cos, tan with respect to a unit circle. The argument to the hyperbolic functions is a hyperbolic angle measure.
The versine or versed sine is a trigonometric function found in some of the earliest (Sanskrit Aryabhatia, [1] Section I) trigonometric tables. The versine of an angle is 1 minus its cosine . There are several related functions, most notably the coversine and haversine .
The following outline is provided as an overview of and topical guide to trigonometry: . Trigonometry – branch of mathematics that studies the relationships between the sides and the angles in triangles.