Returned 84 matches (100 formulae, 52 docs)
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Doc 1
1.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Hyperbolic_law_of_cosines.html
cos α = - cos β cos γ + sin β sin γ cosh a k ,

Doc 2
0.3333
0.3333
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Hyperbolic_triangle.html
cos C = - cos A cos B + sin A sin B cosh c ,

Doc 3
0.2667
1.3535
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Spherical_trigonometry.html
cos A = - cos B cos C + sin B sin C cos a ,
cos B = - cos C cos A + sin C sin A cos b ,
cos C = - cos A cos B + sin A sin B cos c .
cos a = cos b cos c + sin b sin c cos A ,
cos b = cos c cos a + sin c sin a cos B ,
cos c = cos a cos b + sin a sin b cos C ,
cos a = ( cos a cos c + sin a sin c cos B ) cos c + sin b sin c cos A
cos a = cos b cos c + sin b sin c cos A .
cos a sin 2 c = sin a cos c sin c cos B + sin b sin c cos A
Doc 4
0.2667
0.5624
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Law_of_cosines.html
cos A = - cos B cos C + sin B sin C cosh a .
sin ( α + γ ) = sin α cos γ + sin γ cos α
cos 2 γ + sin 2 γ = 1.
c ( sin α cos γ + sin γ cos α ) = b sin γ ,
c = a cos β + b cos α .

Doc 5
0.1806
0.2528
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Spherical_law_of_cosines.html
cos ( A ) = - cos ( B ) cos ( C ) + sin ( B ) sin ( C ) cos ( a )
cos ( c ) = cos ( a ) cos ( b ) + sin ( a ) sin ( b ) cos ( C ) .

Doc 6
0.1511
1.5509
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Proofs_of_trigonometric_identities.html
cos ( α - β ) = cos α cos β + sin α sin β
cos ( α - β ) = cos α cos β + sin α sin β
cos ( α - β ) = cos α cos - β - sin α sin - β
cos ( α + β ) = cos α cos β - sin α sin β
cos ( α + β ) = cos α cos β - sin α sin β
sin ( α - β ) = sin α cos - β + cos α sin - β
e i ( α + β ) = ( cos α cos β - sin α sin β ) + i ( sin α cos β + sin β cos α )
sin ( α + β ) = sin α cos β + cos α sin β
sin ( α + β ) = sin α cos β + sin β cos α
cos ( α + β ) + cos ( α - β ) = cos α cos β - sin α sin β + cos α cos β + sin α sin β = 2 cos α cos β
cos ( α + β ) - cos ( α - β ) = cos α cos β - sin α sin β - cos α cos β - sin α sin β = - 2 sin α sin β
sin ( α - β ) = sin α cos β - cos α sin β
sin ( α - β ) = sin α cos β - cos α sin β
cot ( α + β ) = cos ( α + β ) sin ( α + β ) = cos α cos β - sin α sin β sin α cos β + cos α sin β
tan ( α + β ) = sin ( α + β ) cos ( α + β ) = sin α cos β + cos α sin β cos α cos β - sin α sin β
sin ( α + β ) - sin ( α - β ) = sin α cos β + cos α sin β - sin α cos β + cos α sin β = 2 cos α sin β
cos ( α + β ) = O B = O A - B A = O A - R Q = cos α cos β - sin α sin β

Doc 7
0.1488
0.7948
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Solution_of_triangles.html
a = arccos ( cos α + cos β cos γ sin β sin γ )
a = arccos ( cos α + cos β cos γ sin β sin γ ) ,
c = arccos ( cos a cos b + sin a sin b cos γ )
γ = arccos ( sin α sin β cos c - cos α cos β ) ,
c = arccos ( cos γ + cos α cos β sin α sin β ) .
α = 180 - β - γ
b = arccos ( cos β + cos γ cos α sin γ sin α )
b = arccos ( cos β + cos γ cos α sin γ sin α ) ,
sin γ = c b sin β .
Doc 8
0.1300
0.2734
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Ptolemy's_theorem.html
sin α sin β cos β cos γ + sin α cos 2 β sin γ + cos α sin 2 β cos γ + cos α sin β cos β sin γ
sin ( α + β ) sin ( β + γ ) = sin α sin γ + sin β sin ( α + β + γ )
cos ( x + y ) = cos x cos y - sin x sin y
Doc 9
0.1162
0.1738
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Celestial_coordinate_system.html
sin δ = sin β cos ε + cos β sin ε sin λ
tan α = sin λ cos ε - tan β sin ε cos λ ; { cos δ sin α = cos β sin λ cos ε - sin β sin ε ; cos δ cos α = cos β cos λ .

Doc 10
0.1156
0.4325
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/List_of_trigonometric_identities.html
cos ( α + β ) = cos α cos β - sin α sin β
cos ( α ± β ) = cos α cos β sin α sin β
sin ( α + β ) = sin α cos β + cos α sin β
sin ( α ± β ) = sin α cos β ± cos α sin β
tan ( α + β 2 ) = sin α + sin β cos α + cos β = - cos α - cos β sin α - sin β

Doc 11
0.1156
0.1956
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Machin-like_formula.html
cos ( α + β ) = cos α cos β - sin α sin β
sin ( α + β ) = sin α cos β + cos α sin β

Doc 12
0.1098
0.1098
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Differential_geometry_of_surfaces.html
cos c = cos a cos b + sin a sin b cos γ .

Doc 13
0.1071
0.1071
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Bravais_lattice.html
a b c 1 - cos 2 α - cos 2 β - cos 2 γ + 2 cos α cos β cos γ

Doc 14
0.1070
0.1070
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Solar_zenith_angle.html
sin α s = cos h cos δ cos φ + sin δ sin φ

Doc 15
0.1032
0.3694
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Universal_joint.html
𝐱 ^ 2 = [ - cos β sin γ 2 , cos γ 2 , sin β sin γ 2 ]
ω 2 = ω 1 cos β 1 - sin 2 β cos 2 γ 1
γ 2 = atan2 ( sin γ 1 , cos β cos γ 1 )
a 2 = a 1 cos β 1 - sin 2 β cos 2 γ 1 - ω 1 2 cos β sin 2 β sin 2 γ 1 ( 1 - sin 2 β cos 2 γ 1 ) 2
tan γ 1 = cos β tan γ 2

Doc 16
0.1020
0.1020
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Catenoid.html
y ( u , v ) = - cos θ sinh v cos u + sin θ cosh v sin u

Doc 17
0.0996
0.1584
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Prosthaphaeresis.html
cos a = cos b cos c + sin b sin c cos α
cos a - cos b = - 2 sin ( a + b 2 ) sin ( a - b 2 )

Doc 18
0.0978
0.2666
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Trigonometric_functions.html
cos ( x - y ) = cos x cos y + sin x sin y
cos ( x - y ) = cos x cos y + sin x sin y .
cos ( x + y ) = cos x cos y - sin x sin y ,
Doc 19
0.0924
0.2131
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Wetting.html
γ α θ cos α + γ θ β cos β + γ α β = 0
γ α θ + γ θ β cos θ + γ α β cos α = 0
γ α θ cos θ + γ θ β + γ α β cos β = 0
Doc 20
0.0924
0.2131
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Ideal_surface.html
γ α θ cos α + γ θ β cos β + γ α β = 0
γ α θ + γ θ β cos θ + γ α β cos α = 0
γ α θ cos θ + γ θ β + γ α β cos β = 0
Doc 21
0.0907
0.1813
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Triangle.html
cos 2 α + cos 2 β + cos 2 γ + 2 cos ( α ) cos ( β ) cos ( γ ) = 1 ,
r R = 4 T 2 s a b c = cos α + cos β + cos γ - 1 ;

Doc 22
0.0898
0.0898
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Spherical_harmonics.html
cos ( θ - θ ) = cos θ cos θ + sin θ sin θ

Doc 23
0.0881
0.0881
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Orthonormality.html
cos θ 1 cos θ 2 + sin θ 1 sin θ 2 = 0

Doc 24
0.0849
0.2780
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Plus-minus_sign.html
cos ( A + B ) = cos ( A ) cos ( B ) + sin ( A ) sin ( B )
cos ( A - B ) = cos ( A ) cos ( B ) + sin ( A ) sin ( B )
cos ( A - B ) = cos ( A ) cos ( B ) - sin ( A ) sin ( B )
cos ( A ± B ) = cos ( A ) cos ( B ) sin ( A ) sin ( B )

Doc 25
0.0849
0.0849
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Rifleman's_rule.html
cos ( θ - α ) = cos ( θ ) cos ( α ) + sin ( θ ) sin ( α )

Doc 26
0.0804
0.1505
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Pythagorean_theorem.html
cos ( c R ) = cos ( a R ) cos ( b R ) + sin ( a R ) sin ( b R ) cos γ .
cos 2 θ + sin 2 θ = a 2 + b 2 c 2 = 1 ,

Doc 27
0.0793
0.0793
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Tetrahedron.html
V = a b c 6 1 + 2 cos α cos β cos γ - cos 2 α - cos 2 β - cos 2 γ ,

Doc 28
0.0765
0.0765
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Rigid_rotor.html
( ω x ω y ω z ) = ( - sin β cos γ sin γ 0 sin β sin γ cos γ 0 cos β 0 1 ) ( α ˙ β ˙ γ ˙ ) .

Doc 29
0.0756
0.0756
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Solar_irradiance.html
cos ( c ) = cos ( a ) cos ( b ) + sin ( a ) sin ( b ) cos ( C )

Doc 30
0.0745
0.0745
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Spherical_multipole_moments.html
cos γ = cos θ cos θ + sin θ sin θ cos ( ϕ - ϕ )

Doc 31
0.0743
0.0743
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Geodesics_on_an_ellipsoid.html
tan α 1 = cos β 2 sin ω 12 cos β 1 sin β 2 - sin β 1 cos β 2 cos ω 12 ,

Doc 32
0.0727
0.0727
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Brahmagupta's_formula.html
cos C = - cos A

Doc 33
0.0721
0.0721
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Haversine_formula.html
cos ( c ) = cos ( a ) cos ( b ) + sin ( a ) sin ( b ) cos ( C ) .

Doc 34
0.0714
0.0714
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Green's_function_for_the_three-variable_Laplace_equation.html
cos γ = cos θ cos θ + sin θ sin θ cos ( φ - φ ) .

Doc 35
0.0698
0.0698
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Rayleigh_sky_model.html
cos γ = sin θ s sin θ cos ψ + cos θ s cos θ

Doc 36
0.0679
0.0679
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Sundial.html
sin G = cos L cos D cos R - sin L sin R = - cos L cos D sin I + sin L cos I

Doc 37
0.0667
0.0667
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Riemannian_connection_on_a_surface.html
d α = β γ , d β = γ α , d γ = α β .

Doc 38
0.0662
0.0662
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Classical_central-force_problem.html
s y m b o l φ ^ 𝐫 ^ = - sin φ cos φ + cos φ sin φ = 0

Doc 39
0.0655
0.0655
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Laplace's_equation.html
cos Θ = cos φ cos φ + sin φ sin φ cos ( θ - θ ) .

Doc 40
0.0638
0.0638
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Tridiagonal_matrix.html
cos ( x ) = - cos ( π - x )

Doc 41
0.0622
0.0622
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Abū_al-Wafā'_Būzjānī.html
sin ( α ± β ) = sin α cos β ± cos α sin β

Doc 42
0.0622
0.0622
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Trigonometry.html
cos ( A ± B ) = cos A cos B sin A sin B

Doc 43
0.0622
0.0622
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Clausen_function.html
cos ( x - y ) = cos x cos y - sin x sin y

Doc 44
0.0622
0.0622
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/History_of_trigonometry.html
sin ( α ± β ) = sin α cos β ± cos α sin β

Doc 45
0.0621
0.0621
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Pauli_matrices.html
cos c = cos a cos b - n ^ m ^ sin a sin b ,

Doc 46
0.0619
0.0619
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Spectral_theory_of_ordinary_differential_equations.html
cos β f ( x ) - sin β f ( x ) = 0

Doc 47
0.0619
0.0619
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Phase_detector.html
α - β sin ( α - β ) = sin α cos β - sin β cos α

Doc 48
0.0615
0.0615
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Pentagon.html
= cos 72 cos 18 - sin 72 sin 18

Doc 49
0.0588
0.0588
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Cayley–Hamilton_theorem.html
e i ( θ / 2 ) ( n ^ σ ) = I 2 cos θ / 2 + i ( n ^ σ ) sin θ / 2 ,

Doc 50
0.0542
0.0542
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Vector_algebra_relations.html
𝐀 = 𝐀 ( cos α 𝐢 ^ + cos β 𝐣 ^ + cos γ 𝐤 ^ ) ,

Doc 51
0.0542
0.0542
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Rotation_group_SO(3).html
cos c = cos a cos b - u ^ v ^ sin a sin b ,

Doc 52
0.0541
0.0541
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Trigonometric_tables.html
cos ( x ± y ) = cos ( x ) cos ( y ) sin ( x ) sin ( y )