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埃因霍温理工大学市场开发文凭证书《做证微fuk7778》tAN

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1: 4.14 Definitions and Periodicity
4.14.4 tan z = sin z cos z ,
4.14.7 cot z = cos z sin z = 1 tan z .
The functions tan z , csc z , sec z , and cot z are meromorphic, and the locations of their zeros and poles follow from (4.14.4) to (4.14.7). …
4.14.10 tan ( z + k π ) = tan z .
2: 4.47 Approximations
Clenshaw (1962) and Luke (1975, Chapter 3) give 20D coefficients for ln , exp , sin , cos , tan , cot , arcsin , arctan , arcsinh . Schonfelder (1980) gives 40D coefficients for sin , cos , tan . … Hart et al. (1968) give ln , exp , sin , cos , tan , cot , arcsin , arccos , arctan , sinh , cosh , tanh , arcsinh , arccosh . … Luke (1975, Chapter 3) supplies real and complex approximations for ln , exp , sin , cos , tan , arctan , arcsinh . …
3: 4.21 Identities
4.21.4 tan ( u ± v ) = tan u ± tan v 1 tan u tan v ,
4.21.10 tan u ± tan v = sin ( u ± v ) cos u cos v ,
4.21.26 tan ( z ) = tan z .
4.21.29 tan ( 2 z ) = 2 tan z 1 tan 2 z = 2 cot z cot 2 z 1 = 2 cot z tan z .
If t = tan ( 1 2 z ) , then …
4: 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 , .
5: 4.16 Elementary Properties
Table 4.16.1: Signs of the trigonometric functions in the four quadrants.
Quadrant sin θ , csc θ cos θ , sec θ tan θ , cot θ
Table 4.16.2: Trigonometric functions: quarter periods and change of sign.
x θ 1 2 π ± θ π ± θ 3 2 π ± θ 2 π ± θ
tan x tan θ cot θ ± tan θ cot θ ± tan θ
cot x cot θ tan θ ± cot θ tan θ ± cot θ
Table 4.16.3: Trigonometric functions: interrelations. …
sin θ = a cos θ = a tan θ = a csc θ = a sec θ = a cot θ = a
tan θ a ( 1 a 2 ) 1 / 2 a 1 ( 1 a 2 ) 1 / 2 a ( a 2 1 ) 1 / 2 ( a 2 1 ) 1 / 2 a 1
6: 4.20 Derivatives and Differential Equations
4.20.3 d d z tan z = sec 2 z ,
4.20.5 d d z sec z = sec z tan z ,
4.20.14 w = ( 1 / a ) tan ( a z + c ) ,
7: 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
4.17.2 lim z 0 tan z z = 1 .
8: 4.46 Tables
For 40D values of the first 500 roots of tan x = x , see Robinson (1972). …
9: 4.15 Graphics
See accompanying text
Figure 4.15.3: tan x and cot x . Magnify
See accompanying text
Figure 4.15.10: tan ( x + i y ) . Magnify 3D Help
4.15.2 cot ( x + i y ) = tan ( x + 1 2 π + i y ) ,
10: 19.11 Addition Theorems
tan ( 1 2 ψ ) = ( sin θ ) Δ ( ϕ ) + ( sin ϕ ) Δ ( θ ) cos θ + cos ϕ .
19.11.9 tan θ = 1 / ( k tan ϕ ) .
tan ( 1 2 ψ ) = ( tan θ ) Δ ( θ ) ,
tan θ = tan ( 1 2 ψ ) 1 + cos ψ ( cos ψ ) + Δ ( ψ ) ,