DLMF:

Digital Library of Mathematical Functions

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4 Elementary Functions Trigonometric Functions 4.15 Graphics 4.15 Graphics 4.16 Elementary Properties

Figure 4.15.7 (See in context.)

See accompanying text

(i)

-plane (ii)

-plane


	A	B	C	$\mathrm{\overline{C}}$	D	$\mathrm{\overline{D}}$	E	$\mathrm{\overline{E}}$	F
	0	$\tfrac{1}{2}\pi$	$\tfrac{1}{2}\pi+ir$	$\tfrac{1}{2}\pi-ir$			$-\tfrac{1}{2}\pi+ir$	$-\tfrac{1}{2}\pi-ir$	$-\tfrac{1}{2}\pi$
	0	1	$\mathop{\cosh\/}\nolimits r+i0$	$\mathop{\cosh\/}\nolimits r-i0$	$i\mathop{\sinh\/}\nolimits r$	$-i\mathop{\sinh\/}\nolimits r$	$-\mathop{\cosh\/}\nolimits r+i0$	$-\mathop{\cosh\/}\nolimits r-i0$	−1

Figure 4.15.7: Conformal mapping of sine and inverse sine. $w=\mathop{\sin\/}\nolimits z$ , $z=\mathop{\mathrm{arcsin}\/}\nolimits w$ .

Annotations:

Symbols:: $\mathop{\cosh\/}\nolimits z$ : hyperbolic cosine function, $\mathop{\sinh\/}\nolimits z$ : hyperbolic sine function, $\mathop{\mathrm{arcsin}\/}\nolimits z$ : arcsine function, $\mathop{\sin\/}\nolimits z$ : sine function, : complex variable, : mapping and : real parameter
Keywords:: inverse trigonometric functions, trigonometric functions
Permalink:: http://dlmf.nist.gov/4.15.F7.mag
Encodings:: Magnified png, pdf

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