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arcus sinus (arcsin) jest funkcją odwrotną do funkcji sinus rozpatrywanej na przedziale W przedziale tym sinus jest funkcją rosnącą (zatem różnowartościową), wobec czego ma funkcję odwrotną, która jest określona na przedziale (czyli obrazie przedziału przez funkcję ).
In mathematics, the inverse trigonometric functions (occasionally also called antitrigonometric, [ 1 ]cyclometric, [ 2 ] or arcus functions [ 3 ]) are the inverse functions of the trigonometric functions, under suitably restricted domains.
2. The inverse trigonometric functions: arcsin and arccos The arcsine function is the solution to the equation: z = sinw = eiw − e−iw 2i. ∗In our conventions, the real inverse tangent function, Arctan x, is a continuous single-valued function that varies smoothly from − 1 2π to +2π as x varies from −∞ to +∞. In contrast, Arccotx
We can then reflect the function in the line y = x to produce the inverse function arccos x, shown in Figure 8. Figure 8: A graph of y = arccos x . From Figure 8 we can see that arccos x has a domain of − 1 ≤ x ≤ 1 and a range of 0 ≤ arccos x ≤ π .
The complex inverse trigonometric and hyperbolic functions. In these notes, we examine the inverse trigonometric and hyperbolic functions, where the arguments of these functions can be complex numbers (see e.g. ref. 1). These are all multi-valued functions.
The inverse trigonometric functions are written using arc-prefix like arcsin(x), arccos(x), arctan(x), arccsc(x), arcsec(x), arccot(x). The inverse trigonometric functions are used to find the angle of a triangle from any of the trigonometric functions.
12 sie 2024 · The inverse sine function, \(\sin^{-1} \left(x\right)\), is also called the arcsine function and denoted by \(\arcsin \left(x\right)\). (This terminology reminds us that the output of the inverse sine function is an angle, or the arc on a unit circle determined by that angle, as shown below.)
