# inverse trigonometric functions

(0.014 seconds)

## 1—10 of 97 matching pages

##### 1: 4.23 Inverse Trigonometric Functions
###### §4.23 InverseTrigonometricFunctions
4.23.6 $\operatorname{Arccot}z=\operatorname{Arctan}\left(1/z\right).$
4.23.7 $\operatorname{arccsc}z=\operatorname{arcsin}\left(1/z\right),$
4.23.8 $\operatorname{arcsec}z=\operatorname{arccos}\left(1/z\right).$
4.23.9 $\operatorname{arccot}z=\operatorname{arctan}\left(1/z\right),$ $z\neq\pm\mathrm{i}$.
##### 2: 4.37 Inverse Hyperbolic Functions
4.37.4 $\operatorname{Arccsch}z=\operatorname{Arcsinh}\left(1/z\right),$
4.37.5 $\operatorname{Arcsech}z=\operatorname{Arccosh}\left(1/z\right),$
4.37.7 $\operatorname{arccsch}z=\operatorname{arcsinh}\left(1/z\right),$
4.37.8 $\operatorname{arcsech}z=\operatorname{arccosh}\left(1/z\right).$
4.37.9 $\operatorname{arccoth}z=\operatorname{arctanh}\left(1/z\right),$ $z\neq\pm 1$.
##### 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 $\ln z$, $\operatorname{Ln}z$; 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 $\operatorname{arcsin}z$, $\operatorname{Arcsin}z$, etc. ; the hyperbolic trigonometric (or just hyperbolic) functions $\sinh z$, $\cosh z$, $\tanh z$, $\operatorname{csch}z$, $\operatorname{sech}z$, $\coth z$; the inverse hyperbolic functions $\operatorname{arcsinh}z$, $\operatorname{Arcsinh}z$, etc. …
##### 5: 19.10 Relations to Other Functions
19.10.2 $(\sinh\phi)R_{C}\left(1,{\cosh^{2}}\phi\right)=\operatorname{gd}\left(\phi% \right).$
##### 6: 4.15 Graphics
###### §4.15(i) Real Arguments Figure 4.15.7: Conformal mapping of sine and inverse sine. … Magnify
###### §4.15(iii) Complex Arguments: Surfaces
The corresponding surfaces for $\operatorname{arccos}\left(x+iy\right)$, $\operatorname{arccot}\left(x+iy\right)$, $\operatorname{arcsec}\left(x+iy\right)$ 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. …
##### 10: 4.32 Inequalities
4.32.4 $\operatorname{arctan}x\leq\tfrac{1}{2}\pi\tanh x,$ $x\geq 0$.