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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
.)
Magnify
(i)
z
-plane (ii)
w
-plane
A
B
C
C
¯
D
D
¯
E
E
¯
F
z
0
1
2
π
1
2
π
+
i
r
1
2
π
−
i
r
i
r
−
i
r
−
1
2
π
+
i
r
−
1
2
π
−
i
r
−
1
2
π
w
0
1
cosh
r
+
i
0
cosh
r
−
i
0
i
sinh
r
−
i
sinh
r
−
cosh
r
+
i
0
−
cosh
r
−
i
0
−
1
Figure 4.15.7:
Conformal mapping of sine and inverse sine.
w
=
sin
z
,
z
=
arcsin
w
.
Magnify
ⓘ
Annotations:
Symbols:
π
: the ratio of the circumference of a circle to its diameter
,
z
¯
: complex conjugate
,
cosh
z
: hyperbolic cosine function
,
sinh
z
: hyperbolic sine function
,
i
: imaginary unit
,
arcsin
z
: arcsine function
,
sin
z
: sine function
,
z
: complex variable
,
w
: mapping
and
r
: real parameter
Keywords:
conformal maps
,
inverse trigonometric functions
,
trigonometric functions
Permalink:
http://dlmf.nist.gov/4.15.F7.mag
Encodings:
Magnified png
,
pdf
See also:
Annotations for
§4.15
and
Ch.4