cosine function
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1—10 of 282 matching pages
1: 4.21 Identities
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4.21.25
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- Symbols:
- : cosine function and : complex variable
- A&S Ref:
- 4.3.14
- Permalink:
- http://dlmf.nist.gov/4.21.E25
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.21(iii), §4.21 and Ch.4
4.21.37
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- Symbols:
- : cosine function, : hyperbolic cosine function, : hyperbolic sine function, : imaginary unit, : sine function, : real variable, : real variable and : complex variable
- A&S Ref:
- 4.3.55
- Permalink:
- http://dlmf.nist.gov/4.21.E37
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.21(iv), §4.21 and Ch.4
4.21.38
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- Symbols:
- : cosine function, : hyperbolic cosine function, : hyperbolic sine function, : imaginary unit, : sine function, : real variable, : real variable and : complex variable
- A&S Ref:
- 4.3.56
- Permalink:
- http://dlmf.nist.gov/4.21.E38
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.21(iv), §4.21 and Ch.4
4.21.40
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- Symbols:
- : cosine function, : cotangent function, : hyperbolic cosine function, : hyperbolic sine function, : imaginary unit, : sine function, : real variable, : real variable and : complex variable
- A&S Ref:
- 4.3.58
- Permalink:
- http://dlmf.nist.gov/4.21.E40
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.21(iv), §4.21 and Ch.4
4.21.42
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- Symbols:
- : cosine function, : hyperbolic cosine function, : hyperbolic sine function, : real variable, : real variable and : complex variable
- A&S Ref:
- 4.3.61
- Permalink:
- http://dlmf.nist.gov/4.21.E42
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.21(iv), §4.21 and Ch.4
2: 4.35 Identities
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4.35.34
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- Symbols:
- : cosine function, : hyperbolic cosine function, : hyperbolic sine function, : imaginary unit, : sine function, : real variable, : real variable and : complex variable
- A&S Ref:
- 4.5.49
- Permalink:
- http://dlmf.nist.gov/4.35.E34
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.35(iv), §4.35 and Ch.4
4.35.35
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- Symbols:
- : cosine function, : hyperbolic cosine function, : hyperbolic sine function, : imaginary unit, : sine function, : real variable, : real variable and : complex variable
- A&S Ref:
- 4.5.50
- Permalink:
- http://dlmf.nist.gov/4.35.E35
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.35(iv), §4.35 and Ch.4
4.35.36
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ⓘ
- Symbols:
- : cosine function, : hyperbolic cosine function, : hyperbolic sine function, : hyperbolic tangent function, : imaginary unit, : sine function, : real variable, : real variable and : complex variable
- A&S Ref:
- 4.5.51
- Permalink:
- http://dlmf.nist.gov/4.35.E36
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.35(iv), §4.35 and Ch.4
4.35.39
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ⓘ
- Symbols:
- : cosine function, : hyperbolic cosine function, : hyperbolic sine function, : real variable, : real variable and : complex variable
- A&S Ref:
- 4.5.56
- Permalink:
- http://dlmf.nist.gov/4.35.E39
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.35(iv), §4.35 and Ch.4
4.35.40
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- Symbols:
- : cosine function, : hyperbolic cosine function, : hyperbolic tangent function, : real variable, : real variable and : complex variable
- A&S Ref:
- 4.5.58
- Permalink:
- http://dlmf.nist.gov/4.35.E40
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.35(iv), §4.35 and Ch.4
3: 4.1 Special Notation
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►The main functions treated in this chapter are the logarithm , ; the exponential , ; the circular trigonometric (or just trigonometric) functions
, , , , , ; the inverse trigonometric functions
, , etc.
; the hyperbolic trigonometric (or just hyperbolic) functions
, , , , , ; the inverse hyperbolic functions
, , etc.
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integers. | |
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4: 4.14 Definitions and Periodicity
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4.14.2
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- Defines:
- : cosine function
- Symbols:
- : base of natural logarithm, : imaginary unit and : complex variable
- A&S Ref:
- 4.3.2
- Referenced by:
- (9.5.3)
- Permalink:
- http://dlmf.nist.gov/4.14.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.14 and Ch.4
4.14.4
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- Defines:
- : tangent function
- Symbols:
- : cosine function, : sine function and : complex variable
- A&S Ref:
- 4.3.3
- Referenced by:
- §4.14, §4.45(i)
- Permalink:
- http://dlmf.nist.gov/4.14.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.14 and Ch.4
4.14.6
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- Defines:
- : secant function
- Symbols:
- : cosine function and : complex variable
- A&S Ref:
- 4.3.5
- Permalink:
- http://dlmf.nist.gov/4.14.E6
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.14 and Ch.4
4.14.7
►The functions
and are entire.
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- Defines:
- : cotangent function
- Symbols:
- : cosine function, : sine function, : tangent function and : complex variable
- A&S Ref:
- 4.3.6
- Referenced by:
- §4.14, §4.45(i), §4.45(ii)
- Permalink:
- http://dlmf.nist.gov/4.14.E7
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.14 and Ch.4
5: 4.28 Definitions and Periodicity
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4.28.2
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- Defines:
- : hyperbolic cosine function
- Symbols:
- : base of natural logarithm and : complex variable
- A&S Ref:
- 4.5.2
- Permalink:
- http://dlmf.nist.gov/4.28.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.28 and Ch.4
4.28.4
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- Defines:
- : hyperbolic tangent function
- Symbols:
- : hyperbolic cosine function, : hyperbolic sine function and : complex variable
- A&S Ref:
- 4.5.3
- Permalink:
- http://dlmf.nist.gov/4.28.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.28 and Ch.4
4.28.6
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- Defines:
- : hyperbolic secant function
- Symbols:
- : hyperbolic cosine function and : complex variable
- A&S Ref:
- 4.5.5
- Permalink:
- http://dlmf.nist.gov/4.28.E6
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.28 and Ch.4
4.28.9
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►The functions
and have period , and has period .
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- Symbols:
- : cosine function, : hyperbolic cosine function, : imaginary unit and : complex variable
- A&S Ref:
- 4.5.8
- Permalink:
- http://dlmf.nist.gov/4.28.E9
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.28, §4.28 and Ch.4
6: 4.32 Inequalities
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4.32.1
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- Symbols:
- : hyperbolic cosine function, : hyperbolic sine function and : real variable
- Permalink:
- http://dlmf.nist.gov/4.32.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.32 and Ch.4
4.32.2
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- Symbols:
- : cosine function, : hyperbolic tangent function, : sine function and : real variable
- Permalink:
- http://dlmf.nist.gov/4.32.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.32 and Ch.4
4.32.3
, ,
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- Symbols:
- : hyperbolic cosine function, : hyperbolic sine function, : real variable and : real variable
- Permalink:
- http://dlmf.nist.gov/4.32.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.32 and Ch.4
7: 4.42 Solution of Triangles
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4.42.2
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- Symbols:
- : cosine function, : secant function, : angle, : base and : hypotenuse
- A&S Ref:
- 4.3.147
- Permalink:
- http://dlmf.nist.gov/4.42.E2
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.42(i), §4.42 and Ch.4
4.42.5
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4.42.6
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4.42.8
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- Symbols:
- : cosine function, : sine function, : angle, : arc length, : arc length and : arc length
- A&S Ref:
- 4.3.149
- Permalink:
- http://dlmf.nist.gov/4.42.E8
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.42(iii), §4.42 and Ch.4
4.42.11
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- Symbols:
- : cosine function, : cotangent function, : sine function, : angle, : angle, : arc length and : arc length
- Permalink:
- http://dlmf.nist.gov/4.42.E11
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.42(iii), §4.42 and Ch.4
8: 22.10 Maclaurin Series
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22.10.4
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- Symbols:
- : order not exceeding, : Jacobian elliptic function, : cosine function, : sine function, : complex and : modulus
- A&S Ref:
- 16.13.1
- Referenced by:
- §22.10(ii), §22.20(iii)
- Permalink:
- http://dlmf.nist.gov/22.10.E4
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §22.10(ii), §22.10 and Ch.22
22.10.5
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- Symbols:
- : order not exceeding, : Jacobian elliptic function, : cosine function, : sine function, : complex and : modulus
- A&S Ref:
- 16.13.2
- Referenced by:
- §22.20(iii)
- Permalink:
- http://dlmf.nist.gov/22.10.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §22.10(ii), §22.10 and Ch.22
22.10.7
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- Symbols:
- : order not exceeding, : Jacobian elliptic function, : hyperbolic cosine function, : hyperbolic secant function, : hyperbolic sine function, : hyperbolic tangent function, : complex, : modulus and : complementary modulus
- A&S Ref:
- 16.15.1
- Referenced by:
- §22.10(ii)
- Permalink:
- http://dlmf.nist.gov/22.10.E7
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §22.10(ii), §22.10 and Ch.22
22.10.8
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- Symbols:
- : order not exceeding, : Jacobian elliptic function, : hyperbolic cosine function, : hyperbolic secant function, : hyperbolic sine function, : hyperbolic tangent function, : complex, : modulus and : complementary modulus
- A&S Ref:
- 16.15.2
- Permalink:
- http://dlmf.nist.gov/22.10.E8
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §22.10(ii), §22.10 and Ch.22
22.10.9
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- Symbols:
- : order not exceeding, : Jacobian elliptic function, : hyperbolic cosine function, : hyperbolic secant function, : hyperbolic sine function, : hyperbolic tangent function, : complex, : modulus and : complementary modulus
- A&S Ref:
- 16.15.3
- Referenced by:
- §22.10(ii)
- Permalink:
- http://dlmf.nist.gov/22.10.E9
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §22.10(ii), §22.10 and Ch.22
9: 4.18 Inequalities
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4.18.3
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- Symbols:
- : the ratio of the circumference of a circle to its diameter, : cosine function, : sine function and : real variable
- A&S Ref:
- 4.3.81
- Referenced by:
- §4.18
- Permalink:
- http://dlmf.nist.gov/4.18.E3
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.18, §4.18 and Ch.4
4.18.5
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- Symbols:
- : hyperbolic cosine function, : hyperbolic sine function, : sine function, : real variable and : complex variable
- A&S Ref:
- 4.3.83
- Referenced by:
- §4.18
- Permalink:
- http://dlmf.nist.gov/4.18.E5
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.18, §4.18 and Ch.4
4.18.6
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- Symbols:
- : cosine function, : hyperbolic cosine function, : hyperbolic sine function, : real variable and : complex variable
- A&S Ref:
- 4.3.84
- Permalink:
- http://dlmf.nist.gov/4.18.E6
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.18, §4.18 and Ch.4
4.18.8
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- Symbols:
- : cosine function, : hyperbolic cosine function and : complex variable
- A&S Ref:
- 4.3.86
- Permalink:
- http://dlmf.nist.gov/4.18.E8
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §4.18, §4.18 and Ch.4
10: 10.64 Integral Representations
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10.64.1
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- Symbols:
- : Kelvin function, : the ratio of the circumference of a circle to its diameter, : cosine function, : differential of , : hyperbolic cosine function, : integral, : sine function, : integer and : real variable
- Permalink:
- http://dlmf.nist.gov/10.64.E1
- Encodings:
- pMML, png, TeX
- See also:
- Annotations for §10.64, §10.64 and Ch.10