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NIST
4
Elementary Functions
Trigonometric Functions
4.16
Elementary Properties
4.18
Inequalities
§4.17
Special Values and Limits
ⓘ
Keywords:
limits
,
trigonometric functions
Notes:
See
Hobson (
1928
, pp. 29–32, 53–75)
.
Permalink:
http://dlmf.nist.gov/4.17
See also:
Annotations for
Ch.4
Table 4.17.1:
Trigonometric functions: values at multiples of
1
12
π
.
θ
sin
θ
cos
θ
tan
θ
csc
θ
sec
θ
cot
θ
0
0
1
0
∞
1
∞
π
/
12
1
4
2
(
3
-
1
)
1
4
2
(
3
+
1
)
2
-
3
2
(
3
+
1
)
2
(
3
-
1
)
2
+
3
π
/
6
1
2
1
2
3
1
3
3
2
2
3
3
3
π
/
4
1
2
2
1
2
2
1
2
2
1
π
/
3
1
2
3
1
2
3
2
3
3
2
1
3
3
5
π
/
12
1
4
2
(
3
+
1
)
1
4
2
(
3
-
1
)
2
+
3
2
(
3
-
1
)
2
(
3
+
1
)
2
-
3
π
/
2
1
0
∞
1
∞
0
7
π
/
12
1
4
2
(
3
+
1
)
-
1
4
2
(
3
-
1
)
-
(
2
+
3
)
2
(
3
-
1
)
-
2
(
3
+
1
)
-
(
2
-
3
)
2
π
/
3
1
2
3
-
1
2
-
3
2
3
3
-
2
-
1
3
3
3
π
/
4
1
2
2
-
1
2
2
-
1
2
-
2
-
1
5
π
/
6
1
2
-
1
2
3
-
1
3
3
2
-
2
3
3
-
3
11
π
/
12
1
4
2
(
3
-
1
)
-
1
4
2
(
3
+
1
)
-
(
2
-
3
)
2
(
3
+
1
)
-
2
(
3
-
1
)
-
(
2
+
3
)
π
0
-
1
0
∞
-
1
∞
ⓘ
Symbols:
π
: the ratio of the circumference of a circle to its diameter
,
csc
z
: cosecant function
,
cos
z
: cosine function
,
cot
z
: cotangent function
,
sec
z
: secant function
,
sin
z
: sine function
and
tan
z
: tangent function
Keywords:
special values
,
trigonometric functions
A&S Ref:
4.3.46
Permalink:
http://dlmf.nist.gov/4.17.T1
See also:
Annotations for
§4.17
and
Ch.4
4.17.1
lim
z
→
0
sin
z
z
=
1
,
ⓘ
Symbols:
sin
z
: sine function
and
z
: complex variable
A&S Ref:
4.3.74
Permalink:
http://dlmf.nist.gov/4.17.E1
Encodings:
TeX
,
pMML
,
png
See also:
Annotations for
§4.17
and
Ch.4
4.17.2
lim
z
→
0
tan
z
z
=
1
.
ⓘ
Symbols:
tan
z
: tangent function
and
z
: complex variable
A&S Ref:
4.3.75
Permalink:
http://dlmf.nist.gov/4.17.E2
Encodings:
TeX
,
pMML
,
png
See also:
Annotations for
§4.17
and
Ch.4
4.17.3
lim
z
→
0
1
-
cos
z
z
2
=
1
2
.
ⓘ
Symbols:
cos
z
: cosine function
and
z
: complex variable
Permalink:
http://dlmf.nist.gov/4.17.E3
Encodings:
TeX
,
pMML
,
png
See also:
Annotations for
§4.17
and
Ch.4