About the Project

circular trigonometric functions

AdvancedHelp

(0.040 seconds)

1—10 of 285 matching pages

1: 4.1 Special Notation
k , m , n integers.
The main functions treated in this chapter are the logarithm ln z , 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 arcsin z , Arcsin z , etc. …
2: 4.17 Special Values and Limits
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
3: 4.21 Identities
4.21.1 sin u ± cos u = 2 sin ( u ± 1 4 π ) = ± 2 cos ( u 1 4 π ) .
4.21.35 sin ( n z ) = 2 n 1 k = 0 n 1 sin ( z + k π n ) , n = 1 , 2 , 3 , .
4: 4.22 Infinite Products and Partial Fractions
4.22.1 sin z = z n = 1 ( 1 z 2 n 2 π 2 ) ,
4.22.2 cos z = n = 1 ( 1 4 z 2 ( 2 n 1 ) 2 π 2 ) .
4.22.3 cot z = 1 z + 2 z n = 1 1 z 2 n 2 π 2 ,
4.22.4 csc 2 z = n = 1 ( z n π ) 2 ,
4.22.5 csc z = 1 z + 2 z n = 1 ( 1 ) n z 2 n 2 π 2 .
5: 19.10 Relations to Other Functions
6: 7.5 Interrelations
7.5.3 C ( z ) = 1 2 + f ( z ) sin ( 1 2 π z 2 ) g ( z ) cos ( 1 2 π z 2 ) ,
7.5.4 S ( z ) = 1 2 f ( z ) cos ( 1 2 π z 2 ) g ( z ) sin ( 1 2 π z 2 ) .
7.5.6 e ± 1 2 π i z 2 ( g ( z ) ± i f ( z ) ) = 1 2 ( 1 ± i ) ( C ( z ) ± i S ( z ) ) .
7.5.9 C ( z ) ± i S ( z ) = 1 2 ( 1 ± i ) ( 1 e ± 1 2 π i z 2 w ( i ζ ) ) .
7.5.12 | ( x ) | 2 = 2 + f 2 ( x ) + g 2 ( x ) 2 2 cos ( 1 4 π + 1 2 π x 2 ) f ( x ) 2 2 cos ( 1 4 π 1 2 π x 2 ) g ( x ) , x 0 .
7: 4.25 Continued Fractions
4.25.1 tan z = z 1 z 2 3 z 2 5 z 2 7 , z ± 1 2 π , ± 3 2 π , .
4.25.2 tan ( a z ) = a tan z 1 + ( 1 a 2 ) tan 2 z 3 + ( 4 a 2 ) tan 2 z 5 + ( 9 a 2 ) tan 2 z 7 + , | z | < 1 2 π , a z ± 1 2 π , ± 3 2 π , .
8: 4.14 Definitions and Periodicity
4.14.8 sin ( z + 2 k π ) = sin z ,
4.14.9 cos ( z + 2 k π ) = cos z ,
4.14.10 tan ( z + k π ) = tan z .
9: 10.64 Integral Representations
10.64.1 ber n ( x 2 ) = ( 1 ) n π 0 π cos ( x sin t n t ) cosh ( x sin t ) d t ,
10.64.2 bei n ( x 2 ) = ( 1 ) n π 0 π sin ( x sin t n t ) sinh ( x sin t ) d t .
10: 19.3 Graphics
See accompanying text
Figure 19.3.6: Π ( ϕ , 2 , k ) as a function of k 2 and sin 2 ϕ for 1 k 2 3 , 0 sin 2 ϕ < 1 . …If sin 2 ϕ = 1 ( > k 2 ), then the function reduces to Π ( 2 , k ) with Cauchy principal value K ( k ) Π ( 1 2 k 2 , k ) , which tends to as k 2 1 . … Magnify 3D Help