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inverse trigonometric functions

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1: 4.23 Inverse Trigonometric Functions
§4.23 Inverse Trigonometric Functions
4.23.6 Arccot z = Arctan ( 1 / z ) .
4.23.7 arccsc z = arcsin ( 1 / z ) ,
4.23.8 arcsec z = arccos ( 1 / z ) .
4.23.9 arccot z = arctan ( 1 / z ) , z ± i .
2: 4.37 Inverse Hyperbolic Functions
4.37.4 Arccsch z = Arcsinh ( 1 / z ) ,
4.37.5 Arcsech z = Arccosh ( 1 / z ) ,
4.37.7 arccsch z = arcsinh ( 1 / z ) ,
4.37.8 arcsech z = arccosh ( 1 / z ) .
4.37.9 arccoth z = arctanh ( 1 / z ) , z ± 1 .
3: 4.27 Sums
§4.27 Sums
For sums of trigonometric and inverse trigonometric functions see Gradshteyn and Ryzhik (2000, Chapter 1), Hansen (1975, §§14–42), Oberhettinger (1973), and Prudnikov et al. (1986a, Chapter 5).
4: 4.1 Special Notation
k , m , n integers.
The main purpose of the present chapter is to extend these definitions and properties to complex arguments z . The main functions treated in this chapter are the logarithm ln z , Ln z ; the exponential exp z , e z ; the circular trigonometric (or just trigonometric) functions sin z , cos z , tan z , csc z , sec z , cot z ; the inverse trigonometric functions arcsin z , Arcsin z , etc. ; the hyperbolic trigonometric (or just hyperbolic) functions sinh z , cosh z , tanh z , csch z , sech z , coth z ; the inverse hyperbolic functions arcsinh z , Arcsinh z , etc. …
5: 19.10 Relations to Other Functions
6: 4.15 Graphics
§4.15(i) Real Arguments
See accompanying text
Figure 4.15.7: Conformal mapping of sine and inverse sine. … Magnify
§4.15(iii) Complex Arguments: Surfaces
The corresponding surfaces for arccos ( x + i y ) , arccot ( x + i y ) , arcsec ( x + i y ) can be visualized from Figures 4.15.9, 4.15.11, 4.15.13 with the aid of equations (4.23.16)–(4.23.18).
7: 4.29 Graphics
The surfaces for the complex hyperbolic and inverse hyperbolic functions are similar to the surfaces depicted in §4.15(iii) for the trigonometric and inverse trigonometric functions. …
8: 4.46 Tables
§4.46 Tables
9: 4.47 Approximations
§4.47 Approximations
§4.47(i) Chebyshev-Series Expansions
10: 4.32 Inequalities
4.32.4 arctan x 1 2 π tanh x , x 0 .