tangent
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*1*
α
=
-
*1*
β
*1*
γ
+
*2*
β
*2*
γ
*3*
Search
Returned 98 matches (100 formulae, 80 docs)
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[ documents-by-formula ]
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
0.3981
0.7961
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Riemann's_differential_equation.html
α
+
α
′
+
β
+
β
′
+
γ
+
γ
′
=
1.
α
+
α
′
+
β
+
β
′
+
γ
+
γ
′
=
1.
Doc 3
0.3602
0.3602
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 4
0.2871
0.4235
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Ordinal_arithmetic.html
α
<
β
⇒
γ
+
α
<
γ
+
β
α
<
β
⇒
α
+
γ
≤
β
+
γ
Doc 5
0.2855
0.4233
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Triangle_inequality.html
α
=
π
/
2
-
γ
,
while
β
=
π
/
2
-
γ
/
2
,
2
β
+
γ
=
π
.
Doc 6
0.2781
0.4570
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Universal_joint.html
tan
γ
2
=
cos
β
tan
γ
1
tan
γ
4
=
cos
β
tan
γ
3
tan
γ
1
=
cos
β
tan
γ
2
Doc 7
0.2779
0.2779
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Lotka–Volterra_equation.html
V
=
-
δ
x
+
γ
ln
(
x
)
-
β
y
+
α
ln
(
y
)
.
Doc 8
0.2741
0.2741
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Quantum_group.html
α
α
*
+
μ
2
β
*
β
=
α
*
α
+
β
*
β
=
I
,
Doc 9
0.2691
0.5198
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Differential_geometry_of_surfaces.html
=
α
+
β
+
γ
-
π
,
∫
Δ
K
d
A
=
α
+
β
+
γ
-
π
.
Doc 10
0.2676
0.4742
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Inverse_Galois_problem.html
α
β
+
β
γ
+
γ
α
=
−
2
α
+
β
+
γ
=
−
1
Doc 11
0.2566
0.2566
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Helmholtz_free_energy.html
d
(
log
Z
)
=
-
d
(
β
U
)
+
β
d
U
+
β
X
d
x
Doc 12
0.2507
0.4391
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Rushbrooke_inequality.html
α
,
α
′
,
β
,
γ
,
γ
′
α
′
+
2
β
+
γ
′
≥
2.
Doc 13
0.2507
0.2507
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Widom_scaling.html
α
,
α
′
,
β
,
γ
,
γ
′
Doc 14
0.2480
0.3780
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Surface_tension.html
d
F
=
-
P
d
V
+
γ
d
A
γ
ls
-
γ
sa
=
-
γ
la
cos
θ
Doc 15
0.2427
0.2427
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Constant_k_filter.html
γ
=
α
+
i
β
=
0
+
i
sin
-
1
ω
ω
c
Doc 16
0.2425
0.9998
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
sin
(
α
-
β
)
=
sin
α
cos
-
β
+
cos
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
Doc 17
0.2400
0.2400
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Baker's_theorem.html
Λ
=
β
0
+
β
1
λ
1
+
⋯
+
β
n
λ
n
Doc 18
0.2397
0.2397
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Propagation_constant.html
γ
T
o
t
=
γ
1
+
γ
2
+
γ
3
+
⋯
+
γ
n
Doc 19
0.2376
0.2376
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Bose–Hubbard_model.html
i
=
j
=
k
=
l
,
α
=
β
=
γ
=
δ
=
0
Doc 20
0.2374
0.2374
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Apollonian_circles.html
α
(
x
2
+
y
2
)
-
2
β
x
-
2
γ
y
+
δ
=
0
,
Doc 21
0.2338
0.4260
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/BKL_singularity.html
χ
=
α
-
β
=
k
ln
ξ
+
const
,
1
2
(
α
+
β
+
γ
)
τ
τ
=
α
τ
β
τ
+
α
τ
γ
τ
+
β
τ
γ
τ
.
Doc 22
0.2312
0.2312
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Binomial_approximation.html
=
1
-
α
x
γ
+
(
1
/
2
)
(
α
x
)
2
(
γ
+
1
)
γ
-
…
Doc 23
0.2277
0.4100
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Ordinary_least_squares.html
y
=
X
1
β
1
+
X
2
β
2
+
ε
,
y
i
=
α
+
β
x
i
+
ε
i
.
Doc 24
0.2220
0.2220
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Heun_function.html
ϵ
=
α
+
β
-
γ
-
δ
+
1
Doc 25
0.2193
0.2193
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Comma_category.html
α
=
β
,
α
′
=
β
′
,
g
=
h
Doc 26
0.2170
0.5912
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Gamma_matrices.html
=
2
γ
ρ
γ
ν
-
γ
ν
2
η
μ
ρ
γ
μ
+
4
γ
ν
γ
ρ
=
2
γ
ρ
γ
ν
-
2
γ
ν
γ
ρ
+
4
γ
ν
γ
ρ
=
2
γ
ν
-
4
γ
ν
=
-
2
γ
ν
.
Doc 27
0.2136
0.3532
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Chevalley_basis.html
β
+
α
≺
γ
+
α
β
0
+
γ
0
=
β
+
γ
Doc 28
0.2127
0.2127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Cyclic_quadrilateral.html
α
+
γ
=
β
+
δ
=
π
=
180
∘
.
Doc 29
0.2075
0.2075
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Circumconic_and_inconic.html
α
=
β
=
γ
=
1
/
3.
Doc 30
0.2066
0.2066
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Solution_of_triangles.html
α
+
β
+
γ
=
180
∘
Doc 31
0.2054
0.6631
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Law_of_cosines.html
α
+
β
+
γ
=
180.
sin
(
α
+
γ
)
=
sin
α
cos
γ
+
sin
γ
cos
α
a
2
=
a
c
cos
β
+
a
b
cos
γ
,
b
2
=
b
c
cos
α
+
a
b
cos
γ
.
Doc 32
0.2050
0.5434
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Parameterized_post-Newtonian_formalism.html
ζ
2
=
2
β
+
2
β
2
-
3
γ
-
1
α
1
=
7
Δ
1
+
Δ
2
-
4
γ
-
4
α
3
=
4
β
1
-
2
γ
-
2
-
ζ
Doc 33
0.2034
0.2034
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Normal_variance-mean_mixture.html
Y
=
α
+
β
V
+
σ
V
X
,
Doc 34
0.1996
0.1996
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/KPP-type_equation.html
u
t
-
α
u
-
β
u
2
+
γ
u
3
=
0
Doc 35
0.1954
0.1954
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Berry_connection_and_curvature.html
γ
~
n
(
t
)
=
γ
n
(
t
)
+
β
(
t
)
-
β
(
0
)
Doc 36
0.1953
0.1953
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Student's_t-test.html
Y
=
α
+
β
x
+
ε
,
Doc 37
0.1942
0.1942
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
Doc 38
0.1942
0.1942
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
Doc 39
0.1942
0.1942
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/Magnetic_anisotropy.html
α
2
+
β
2
+
γ
2
=
1
Doc 40
0.1934
0.1934
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Solow_residual.html
y
=
C
+
β
k
+
γ
ℓ
+
ε
.
Doc 41
0.1919
0.1919
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Motor_variable.html
w
=
α
z
+
β
γ
z
+
δ
where
α
,
β
,
γ
,
δ
Doc 42
0.1904
0.1904
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Endogeneity_(econometrics).html
y
i
=
α
+
β
x
i
+
γ
z
i
+
u
i
Doc 43
0.1896
0.1896
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Duffin–Kemmer–Petiau_algebra.html
β
a
γ
+
γ
β
a
=
β
a
Doc 44
0.1894
0.1894
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Convex_conjugate.html
g
(
x
)
=
α
+
β
x
+
γ
⋅
f
(
λ
x
+
δ
)
Doc 45
0.1891
0.1891
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Darlington_transistor.html
β
Darlington
=
β
1
⋅
β
2
+
β
1
+
β
2
Doc 46
0.1875
0.5954
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/List_of_relativistic_equations.html
γ
v
t
′
=
γ
2
v
t
-
γ
2
x
+
x
x
′
=
γ
x
-
γ
β
c
t
c
t
′
=
γ
c
t
-
γ
β
x
γ
v
t
′
=
γ
2
v
t
-
γ
2
β
2
x
Doc 47
0.1874
0.1874
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Window_function.html
α
=
0.54
,
β
=
1
-
α
=
0.46
,
Doc 48
0.1849
0.1849
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/List_of_trigonometric_identities.html
sin
(
α
+
β
)
=
sin
α
cos
β
+
cos
α
sin
β
Doc 49
0.1849
0.1849
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Machin-like_formula.html
sin
(
α
+
β
)
=
sin
α
cos
β
+
cos
α
sin
β
Doc 50
0.1823
0.1823
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Ecological_fallacy.html
Y
i
=
α
+
β
X
i
+
u
i
,
Doc 51
0.1823
0.1823
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Prediction_interval.html
y
d
=
α
+
β
x
d
+
ϵ
d
.
Doc 52
0.1823
0.1823
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Simple_linear_regression.html
y
i
=
α
+
β
x
i
+
ε
i
.
Doc 53
0.1814
0.1814
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Roll's_critique.html
E
(
R
i
)
=
α
+
β
1
F
1
+
…
+
β
N
F
N
.
Doc 54
0.1810
0.1810
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Choice_model_simulation.html
U
i
=
α
P
i
+
β
D
i
+
γ
Y
+
ε
i
Doc 55
0.1799
0.1799
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Adomian_decomposition_method.html
u
=
α
+
β
x
+
γ
x
2
/
2
-
L
-
1
N
u
Doc 56
0.1771
0.1771
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Geometry_index.html
τ
5
=
β
-
α
60
∘
≈
-
0.01667
α
+
0.01667
β
Doc 57
0.1760
0.1760
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Triangle.html
r
R
=
4
T
2
s
a
b
c
=
cos
α
+
cos
β
+
cos
γ
-
1
;
Doc 58
0.1753
0.1753
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Brocard_points.html
cot
ω
=
cot
α
+
cot
β
+
cot
γ
.
Doc 59
0.1747
0.5538
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Rotation_group_SO(3).html
Z
=
α
X
+
β
Y
+
γ
[
X
,
Y
]
,
Z
=
α
′
X
+
β
′
Y
+
γ
′
[
X
,
Y
]
,
ζ
′
=
α
ζ
+
β
γ
ζ
+
δ
,
α
δ
-
β
γ
≠
0.
(
α
β
γ
δ
)
,
α
δ
-
β
γ
=
1
,
Doc 60
0.1747
0.1747
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Rotation_matrix.html
Z
=
α
X
+
β
Y
+
γ
[
X
,
Y
]
,
Doc 61
0.1734
0.1734
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Homogeneous_differential_equation.html
t
=
x
+
α
;
z
=
y
+
β
.
Doc 62
0.1643
0.1643
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/De_Rham_cohomology.html
ω
=
d
α
+
δ
β
+
γ
Doc 63
0.1632
0.1632
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Polynomial_least_squares.html
z
=
y
+
ε
=
α
+
β
t
+
ε
Doc 64
0.1622
0.1622
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Pole–zero_plot.html
s
=
α
1
=
-
3
+
4
j
Doc 65
0.1600
0.1600
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Ordinal_collapsing_function.html
α
=
δ
β
1
γ
1
+
⋯
+
δ
β
k
γ
k
Doc 66
0.1597
0.1597
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Qutrit.html
|
ψ
⟩
=
α
|
0
⟩
+
β
|
1
⟩
+
γ
|
2
⟩
Doc 67
0.1565
0.1565
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Bhargava_cube.html
x
↦
α
x
+
β
y
,
y
↦
γ
x
+
δ
y
Doc 68
0.1543
0.1543
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Boundary-incompressible_surface.html
α
∩
β
=
∂
α
=
∂
β
Doc 69
0.1521
0.1521
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Hurwitz_zeta_function.html
γ
0
(
1
)
=
-
ψ
(
1
)
=
γ
0
=
γ
Doc 70
0.1505
0.1505
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Recurrence_relation.html
λ
1
⋅
λ
2
=
α
2
+
β
2
=
-
B
,
Doc 71
0.1495
0.1495
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Two-way_analysis_of_variance.html
μ
i
j
=
μ
+
α
i
+
β
j
+
γ
i
j
Doc 72
0.1484
0.1484
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Prisoner's_dilemma.html
α
s
x
+
β
s
y
+
γ
=
0
Doc 73
0.1411
0.1411
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Plasma_fusion_preface.html
r
1
,
2
=
-
b
+
/
-
j
γ
Doc 74
0.1410
0.1410
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Modulational_instability.html
β
2
2
ω
m
2
+
2
γ
P
β
2
<
0
Doc 75
0.1382
0.1382
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Circumscribed_circle.html
P
c
=
α
P
1
+
β
P
2
+
γ
P
3
Doc 76
0.1355
0.1355
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Differential_form.html
α
∧
(
β
+
γ
)
=
α
∧
β
+
α
∧
γ
.
Doc 77
0.1335
0.1335
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Douady_rabbit.html
γ
=
2
-
γ
D
=
-
.55268
+
.959456
i
Doc 78
0.1329
0.1329
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Quantum_spacetime.html
det
q
(
α
β
γ
δ
)
=
α
δ
-
q
2
γ
β
Doc 79
0.1295
0.1295
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Epidemic_model.html
d
S
d
T
=
B
-
β
S
I
-
μ
S
+
γ
I
Doc 80
0.1090
0.1090
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Weighted_constraint_satisfaction_problem.html
α
⊖
β
=
α
-
β