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Therefore, the result ranges of the inverse functions are proper (i.e. strict) subsets of the domains of the original functions. For example, using function in the sense of multivalued functions, just as the square root function = could be defined from =, the function = is defined so that =.
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.
Arcsine Arccosine.svg - a nice plot of the arcsine and the arccosine function Image title Arcsine(arcsin)-function + Arcsine(arccos)-function from Wikimedia Commons plot-range: complete functions plotted with cubic bezier-curves in several intervalls the bezier-controll-points are calculated to give a very accurate result.
For example, the sine, cosine ... The following table summarizes the properties of the graphs of the six main trigonometric functions: [40] ... arcsine: y = arcsin(x)
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.
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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
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