tangent
Not Supported
p
=
-
x
±
x
x0
-
4
(
x1
)
(
x2
x3
-
y
)
2
(
-
g
x
2
x4
)
Search
Returned 95 matches (100 formulae, 74 docs)
Lookup 735.734 ms, Re-ranking 1489.674 ms
Found 1759181 tuple postings, 216911 formulae, 22624 documents
[ formulas ]
[ documents ]
[ documents-by-formula ]
p
=
-
x
±
x
2
-
4
(
-
g
x
2
2
v
2
)
(
-
g
x
2
2
v
2
-
y
)
2
(
-
g
x
2
2
v
2
)
Doc 1
0.9245, -16.0000, 22.0000, 2.3747
testing/wikipedia/v3/09833.html
x
=
-
b
±
b
2
-
4
a
c
2
a
⇒
x
=
y
2
y
1
=
-
1
2
±
1
2
2
-
4
(
1
2
)
(
-
F
r
1
2
)
2
(
1
2
)
=
-
1
2
±
1
4
+
2
F
r
1
2
1
Doc 2
0.4660, -55.0000, 12.0000, 0.6340
testing/wikipedia/v3/27191.html
f
′′
(
x
)
=
(
q
p
)
(
q
p
-
1
)
x
q
p
-
2
Doc 3
0.2979, -12.0000, 4.0000, 0.2979
testing/wikipedia/v3/00467.html
R
i
-
(
1
+
i
)
n
(
R
i
-
P
)
Doc 4
0.2821, -7.0000, 4.0000, 0.2821
testing/wikipedia/v3/12489.html
p
=
v
2
±
v
4
-
g
(
g
x
2
+
2
y
v
2
)
g
x
Doc 1
0.9245, -16.0000, 22.0000, 2.3747
testing/wikipedia/v3/09833.html
tan
θ
=
v
2
±
v
4
-
g
(
g
x
2
+
2
y
v
2
)
g
x
Doc 1
0.9245, -16.0000, 22.0000, 2.3747
testing/wikipedia/v3/09833.html
θ
=
arctan
(
v
2
±
v
4
-
g
(
g
x
2
+
2
y
v
2
)
g
x
)
Doc 1
0.9245, -16.0000, 22.0000, 2.3747
testing/wikipedia/v3/09833.html
θ
=
tan
-
1
(
v
2
±
v
4
-
g
(
g
x
2
+
2
y
v
2
)
g
x
)
Doc 1
0.9245, -16.0000, 22.0000, 2.3747
testing/wikipedia/v3/09833.html
z
=
1
2
(
x
2
+
y
2
)
(
1
a
2
-
1
b
2
)
+
x
y
(
1
a
2
+
1
b
2
)
Doc 5
0.2595, -26.0000, 4.0000, 0.2595
testing/wikipedia/v3/02322.html
(
1
x
)
(
1
y
)
Doc 6
0.2062, -2.0000, 3.0000, 0.4124
testing/wikipedia/v3/00687.html
(
1
y
)
(
1
x
)
Doc 6
0.2062, -2.0000, 3.0000, 0.4124
testing/wikipedia/v3/00687.html
(
p
+
r
2
)
(
q
+
s
2
)
Doc 7
0.2062, -6.0000, 3.0000, 0.2062
testing/wikipedia/v3/03760.html
(
p
-
1
2
)
(
q
-
1
2
)
,
Doc 9
0.2062, -7.0000, 3.0000, 0.2062
testing/wikipedia/v3/11626.html
=
(
3
331
)
(
5
331
)
(
823
331
)
Doc 8
0.2062, -7.0000, 3.0000, 0.6186
testing/wikipedia/v3/00617.html
=
(
3
331
)
(
5
331
)
(
161
331
)
Doc 8
0.2062, -7.0000, 3.0000, 0.6186
testing/wikipedia/v3/00617.html
(
a
m
n
)
=
(
a
m
)
(
a
n
)
Doc 11
0.2062, -8.0000, 3.0000, 0.4124
testing/wikipedia/v3/02166.html
(
a
n
m
)
=
(
a
n
)
(
a
m
)
Doc 10
0.2062, -8.0000, 3.0000, 0.4124
testing/wikipedia/v3/06302.html
(
a
b
n
)
=
(
a
n
)
(
b
n
)
Doc 10
0.2062, -8.0000, 3.0000, 0.4124
testing/wikipedia/v3/06302.html
Doc 11
0.2062, -8.0000, 3.0000, 0.4124
testing/wikipedia/v3/02166.html
(
v
c
)
2
(
r
r
s
-
1
)
=
1
2
.
Doc 12
0.2062, -11.0000, 4.0000, 0.3359
testing/wikipedia/v3/02950.html
=
(
3
331
)
(
5
331
)
(
7
331
)
(
23
331
)
Doc 8
0.2062, -7.0000, 3.0000, 0.6186
testing/wikipedia/v3/00617.html
(
α
𝔭
)
n
(
β
𝔭
)
n
=
(
α
β
𝔭
)
n
Doc 13
0.2062, -11.0000, 3.0000, 0.2062
testing/wikipedia/v3/28112.html
log
(
G
(
1
2
+
z
)
G
(
1
2
-
z
)
)
=
Doc 14
0.2062, -12.0000, 3.0000, 0.2062
testing/wikipedia/v3/09909.html
D
1
=
(
h
1
-
1
γ
)
(
1
h
1
-
1
h
2
)
Doc 15
0.2062, -14.0000, 4.0000, 0.2062
testing/wikipedia/v3/27298.html
K
s
p
=
(
N
A
(
f
)
V
)
x
(
N
B
(
f
)
V
)
y
Doc 16
0.2062, -14.0000, 3.0000, 0.4124
testing/wikipedia/v3/13717.html
K
s
p
=
(
N
A
(
Δ
)
V
)
x
(
N
B
(
Δ
)
V
)
y
Doc 16
0.2062, -14.0000, 3.0000, 0.4124
testing/wikipedia/v3/13717.html
0
=
-
g
x
2
2
v
2
p
2
+
x
p
-
g
x
2
2
v
2
-
y
Doc 1
0.9245, -16.0000, 22.0000, 2.3747
testing/wikipedia/v3/09833.html
0
=
-
g
x
2
2
v
2
tan
2
θ
+
x
tan
θ
-
g
x
2
2
v
2
-
y
Doc 1
0.9245, -16.0000, 22.0000, 2.3747
testing/wikipedia/v3/09833.html
σ
x
x
=
-
μ
b
2
π
(
1
-
ν
)
y
(
3
x
2
+
y
2
)
(
x
2
+
y
2
)
2
Doc 17
0.2062, -24.0000, 4.0000, 0.2062
testing/wikipedia/v3/06599.html
F
(
ε
)
=
ε
2
∫
0
1
(
2
u
-
ln
(
1
u
)
-
2
)
e
-
ε
u
d
u
Doc 19
0.2062, -24.0000, 3.0000, 0.2062
testing/wikipedia/v3/28186.html
B
n
∼
1
n
(
n
W
(
n
)
)
n
+
1
2
exp
(
n
W
(
n
)
-
n
-
1
)
.
Doc 18
0.2062, -24.0000, 3.0000, 0.2062
testing/wikipedia/v3/02890.html
ζ
Ai
(
1
)
=
-
3
-
2
/
3
Γ
(
2
3
)
Γ
(
4
3
)
.
Doc 20
0.1931, -16.0000, 5.0000, 0.1931
testing/wikipedia/v3/25445.html
v
1
′
(
1
2
)
=
v
2
′
(
1
2
)
Doc 21
0.1818, -9.0000, 2.0000, 0.3240
testing/wikipedia/v3/21848.html
μ
λ
=
sin
(
A
+
D
λ
2
)
sin
(
A
2
)
Doc 22
0.1818, -11.0000, 4.0000, 0.1818
testing/wikipedia/v3/17328.html
ϕ
(
p
)
=
(
x
0
ℏ
π
)
1
/
2
⋅
exp
(
-
x
0
2
(
p
-
p
0
)
2
2
ℏ
2
)
,
Doc 23
0.1818, -26.0000, 4.0000, 0.1818
testing/wikipedia/v3/01067.html
-
(
∂
T
∂
V
)
P
(
∂
S
∂
P
)
V
Doc 24
0.1681, -10.0000, 3.0000, 0.1681
testing/wikipedia/v3/06999.html
(
∂
z
∂
x
)
y
(
∂
x
∂
z
)
y
=
1.
Doc 25
0.1681, -11.0000, 3.0000, 0.6055
testing/wikipedia/v3/04601.html
=
2
(
t
a
-
floor
(
1
2
+
t
a
)
)
Doc 26
0.1681, -11.0000, 3.0000, 0.1681
testing/wikipedia/v3/01650.html
(
∂
z
∂
x
)
y
=
-
(
∂
z
∂
y
)
x
(
∂
y
∂
x
)
z
Doc 27
0.1681, -18.0000, 3.0000, 0.4374
testing/wikipedia/v3/14685.html
(
∂
x
∂
y
)
z
(
∂
y
∂
z
)
x
(
∂
z
∂
x
)
y
=
-
1
Doc 27
0.1681, -18.0000, 3.0000, 0.4374
testing/wikipedia/v3/14685.html
(
∂
z
∂
x
)
y
(
∂
x
∂
y
)
z
=
-
(
∂
z
∂
y
)
x
.
Doc 25
0.1681, -11.0000, 3.0000, 0.6055
testing/wikipedia/v3/04601.html
(
8
)
(
∂
z
∂
y
)
x
=
-
(
∂
z
∂
x
)
y
(
∂
x
∂
y
)
z
Doc 25
0.1681, -11.0000, 3.0000, 0.6055
testing/wikipedia/v3/04601.html
q
2
g
(
1
y
1
-
1
y
2
)
=
1
2
(
y
2
2
-
y
1
2
)
Doc 2
0.4660, -55.0000, 12.0000, 0.6340
testing/wikipedia/v3/27191.html
q
2
g
(
1
y
1
-
1
y
2
)
=
1
2
(
y
z
2
-
y
1
2
)
Doc 28
0.1681, -21.0000, 3.0000, 0.1681
testing/wikipedia/v3/26075.html
|
x
-
1
2
(
a
c
+
b
d
)
|
=
1
2
(
b
d
-
a
c
)
Doc 29
0.1681, -21.0000, 3.0000, 0.1681
testing/wikipedia/v3/27724.html
1
(
u
+
A
)
(
u
-
A
)
=
1
2
A
(
1
u
-
A
-
1
u
+
A
)
Doc 30
0.1681, -22.0000, 3.0000, 0.1681
testing/wikipedia/v3/05353.html
E
I
d
4
w
d
x
4
-
3
2
E
A
(
d
w
d
x
)
2
(
d
2
w
d
x
2
)
=
q
(
x
)
Doc 31
0.1681, -29.0000, 3.0000, 0.1681
testing/wikipedia/v3/09923.html
f
(
x
)
=
2
β
α
2
Γ
(
α
2
)
x
α
-
1
exp
(
-
β
x
2
)
Doc 32
0.1519, -19.0000, 4.0000, 0.1519
testing/wikipedia/v3/12246.html
r
x
y
=
x
y
¯
-
x
¯
y
¯
(
x
2
¯
-
x
¯
2
)
(
y
2
¯
-
y
¯
2
)
Doc 33
0.1519, -20.0000, 4.0000, 0.1519
testing/wikipedia/v3/10770.html
w
=
∑
i
(
x
i
-
x
¯
)
(
d
i
-
d
¯
)
∑
i
(
x
i
-
x
¯
)
2
Doc 35
0.1519, -20.0000, 3.0000, 0.1519
testing/wikipedia/v3/09141.html
f
=
v
2
(
ℓ
L
x
)
2
+
(
m
L
y
)
2
+
(
n
L
z
)
2
Doc 34
0.1519, -20.0000, 3.0000, 0.1519
testing/wikipedia/v3/12330.html
S
2
=
2
m
[
m
(
2
)
-
x
¯
2
2
x
¯
]
2
=
m
(
d
~
-
1
)
2
2
Doc 36
0.1519, -21.0000, 1.0000, 0.1519
testing/wikipedia/v3/29923.html
f
(
x
;
k
)
=
2
1
-
k
2
x
k
-
1
e
-
x
2
2
Γ
(
k
2
)
Doc 37
0.1519, -22.0000, 5.0000, 0.1519
testing/wikipedia/v3/09559.html
2
π
ε
l
arcosh
(
d
a
)
=
2
π
ε
l
ln
(
d
a
+
d
2
a
2
-
1
)
Doc 38
0.1519, -24.0000, 4.0000, 0.1519
testing/wikipedia/v3/02275.html
v
1
(
1
2
)
=
v
2
(
1
2
)
Doc 21
0.1818, -9.0000, 2.0000, 0.3240
testing/wikipedia/v3/21848.html
S
N
(
f
)
=
N
0
2
(
1
+
(
w
B
)
2
)
Doc 39
0.1422, -12.0000, 2.0000, 0.1422
testing/wikipedia/v3/06533.html
tan
A
=
(
(
-
∂
z
∂
y
)
(
∂
z
∂
x
)
)
Doc 40
0.1422, -13.0000, 3.0000, 0.1422
testing/wikipedia/v3/00438.html
d
y
d
x
=
-
4
x
3
4
y
=
-
x
3
y
Doc 41
0.1422, -14.0000, 3.0000, 0.1422
testing/wikipedia/v3/03420.html
Q
=
2
N
2
N
-
1
=
1
2
sinh
(
ln
(
2
)
2
N
)
Doc 42
0.1422, -17.0000, 2.0000, 0.1422
testing/wikipedia/v3/26628.html
∫
(
x
2
2
+
y
x
)
d
y
=
y
x
2
2
+
x
y
2
2
Doc 43
0.1422, -18.0000, 4.0000, 0.1422
testing/wikipedia/v3/04191.html
(
1
2
(
x
-
1
x
)
)
2
+
1
=
(
1
2
(
x
+
1
x
)
)
2
,
Doc 44
0.1422, -21.0000, 2.0000, 0.1422
testing/wikipedia/v3/00703.html
d
d
x
(
1
x
3
+
4
x
)
=
-
3
x
2
-
4
(
x
3
+
4
x
)
2
.
Doc 45
0.1422, -23.0000, 4.0000, 0.4016
testing/wikipedia/v3/13099.html
Q
(
x
)
=
1
2
-
1
2
erf
(
x
2
)
=
1
2
erfc
(
x
2
)
.
Doc 46
0.1422, -23.0000, 3.0000, 0.1422
testing/wikipedia/v3/02688.html
ϕ
=
arctan
(
y
x
)
=
arccos
(
x
x
2
+
y
2
)
=
arcsin
(
y
x
2
+
y
2
)
Doc 47
0.1422, -24.0000, 2.0000, 0.1422
testing/wikipedia/v3/13693.html
1
2
(
x
2
-
4
x
+
2
)
Doc 48
0.1297, -7.0000, 3.0000, 0.1297
testing/wikipedia/v3/07059.html
f
(
x
)
=
x
3
-
2
x
2
(
x
2
-
5
)
Doc 49
0.1297, -12.0000, 4.0000, 0.1297
testing/wikipedia/v3/04272.html
sin
(
x
2
)
=
±
1
2
(
1
-
cos
x
)
Doc 50
0.1297, -12.0000, 2.0000, 0.1297
testing/wikipedia/v3/02375.html
ϕ
=
tan
-
1
(
y
1
-
y
2
x
1
-
x
2
)
Doc 51
0.1297, -13.0000, 2.0000, 0.2595
testing/wikipedia/v3/23272.html
η
p
=
2
(
v
v
e
)
1
+
(
v
v
e
)
2
Doc 52
0.1297, -14.0000, 3.0000, 0.1297
testing/wikipedia/v3/00547.html
X
=
1
2
[
(
T
β
)
0.5
-
(
T
β
)
-
0.5
]
Doc 53
0.1297, -14.0000, 3.0000, 0.1297
testing/wikipedia/v3/21706.html
haversin
(
θ
)
=
sin
2
(
θ
2
)
=
1
-
cos
(
θ
)
2
Doc 54
0.1297, -14.0000, 2.0000, 0.1297
testing/wikipedia/v3/05723.html
r
r
s
(
v
c
)
2
(
1
-
r
s
r
)
=
1
2
Doc 12
0.2062, -11.0000, 4.0000, 0.3359
testing/wikipedia/v3/02950.html
(
J
0
3
f
)
(
x
)
=
-
x
-
x
2
2
-
x
3
3
Doc 55
0.1297, -16.0000, 2.0000, 0.1297
testing/wikipedia/v3/08705.html
ω
±
=
ω
c
2
±
(
ω
c
2
)
2
-
ω
t
2
2
Doc 57
0.1297, -17.0000, 3.0000, 0.1297
testing/wikipedia/v3/10151.html
e
=
(
x
0
-
x
)
2
+
(
y
0
-
y
)
2
2
a
(
17
)
Doc 56
0.1297, -17.0000, 3.0000, 0.2206
testing/wikipedia/v3/23312.html
f
(
x
)
=
1
+
2
(
1
x
+
x
x
2
-
4
x
+
8
)
Doc 58
0.1297, -17.0000, 3.0000, 0.1297
testing/wikipedia/v3/03370.html
=
1
θ
k
Γ
(
k
)
(
1
y
)
k
+
1
exp
(
-
1
θ
y
)
Doc 60
0.1297, -18.0000, 3.0000, 0.1297
testing/wikipedia/v3/09040.html
d
d
x
(
1
g
(
x
)
)
=
-
g
′
(
x
)
(
g
(
x
)
)
2
Doc 45
0.1422, -23.0000, 4.0000, 0.4016
testing/wikipedia/v3/13099.html
y
=
R
(
2
(
x
L
)
-
K
′
(
x
L
)
2
2
-
K
′
)
Doc 59
0.1297, -18.0000, 3.0000, 0.1297
testing/wikipedia/v3/09114.html
[
cos
(
θ
2
)
-
sin
(
θ
2
)
sin
(
θ
2
)
cos
(
θ
2
)
]
Doc 61
0.1297, -18.0000, 2.0000, 0.1297
testing/wikipedia/v3/03193.html
K
=
2
(
Γ
(
n
-
1
2
)
)
2
(
Γ
(
n
-
2
2
)
)
2
.
Doc 62
0.1297, -19.0000, 2.0000, 0.2595
testing/wikipedia/v3/26874.html
d
d
x
(
1
g
(
x
)
)
=
d
d
x
(
f
(
x
)
g
(
x
)
)
Doc 45
0.1422, -23.0000, 4.0000, 0.4016
testing/wikipedia/v3/13099.html
1
+
2
(
1
8
)
+
4
(
1
8
)
2
+
8
(
1
8
)
3
+
⋯
.
Doc 64
0.1297, -20.0000, 3.0000, 0.1297
testing/wikipedia/v3/00449.html
1
+
7
x
+
12
x
2
-
4
x
3
(
1
-
x
2
)
(
1
-
16
x
2
)
Doc 63
0.1297, -20.0000, 3.0000, 0.2310
testing/wikipedia/v3/24194.html
K
=
2
(
Γ
(
N
-
t
2
)
)
2
(
Γ
(
N
-
t
-
1
2
)
)
2
Doc 62
0.1297, -19.0000, 2.0000, 0.2595
testing/wikipedia/v3/26874.html
ln
(
p
(
z
2
)
p
(
z
1
)
)
=
-
g
R
⋅
T
¯
(
z
2
-
z
1
)
Doc 65
0.1297, -21.0000, 3.0000, 0.1297
testing/wikipedia/v3/16091.html
θ
=
tan
-
1
(
(
x
1
-
x
2
)
2
+
(
y
1
-
y
2
)
2
z
1
-
z
2
)
Doc 51
0.1297, -13.0000, 2.0000, 0.2595
testing/wikipedia/v3/23272.html
π
x
2
6
-
3
x
2
-
(
x
2
)
2
2
+
x
2
-
(
x
2
)
2
2
Doc 66
0.1297, -26.0000, 3.0000, 0.1297
testing/wikipedia/v3/00025.html
∫
0
∞
x
n
e
-
a
x
2
d
x
=
Γ
(
(
n
+
1
)
2
)
2
a
(
n
+
1
)
2
Doc 67
0.1297, -26.0000, 3.0000, 0.1297
testing/wikipedia/v3/05600.html
α
(
x
)
=
x
+
x
2
+
4
2
,
β
(
x
)
=
x
-
x
2
+
4
2
Doc 68
0.1087, -22.0000, 4.0000, 0.1087
testing/wikipedia/v3/05130.html
1
+
7
x
(
1
-
x
2
)
(
1
-
16
x
2
)
Doc 63
0.1297, -20.0000, 3.0000, 0.2310
testing/wikipedia/v3/24194.html
(
d
x
d
t
)
2
+
(
d
y
d
t
)
2
Doc 69
0.1013, -12.0000, 2.0000, 0.2025
testing/wikipedia/v3/04037.html
(
∂
z
∂
x
)
y
=
1
(
∂
x
∂
z
)
y
.
Doc 25
0.1681, -11.0000, 3.0000, 0.6055
testing/wikipedia/v3/04601.html
p
=
∂
g
∂
z
(
∂
g
∂
x
)
2
+
(
∂
g
∂
y
)
2
Doc 70
0.1013, -20.0000, 3.0000, 0.1013
testing/wikipedia/v3/25915.html
(
∂
x
∂
y
)
z
=
-
(
∂
z
∂
y
)
x
(
∂
z
∂
x
)
y
Doc 27
0.1681, -18.0000, 3.0000, 0.4374
testing/wikipedia/v3/14685.html
1
r
=
(
d
2
x
d
s
2
)
2
+
(
d
2
y
d
s
2
)
2
Doc 71
0.1013, -20.0000, 2.0000, 0.1013
testing/wikipedia/v3/25618.html
A
y
=
2
π
∫
a
b
x
(
t
)
(
d
x
d
t
)
2
+
(
d
y
d
t
)
2
d
t
,
Doc 69
0.1013, -12.0000, 2.0000, 0.2025
testing/wikipedia/v3/04037.html
d
(
d
(
d
(
f
(
x
)
)
d
x
)
d
x
)
d
x
,
Doc 72
0.0909, -16.0000, 2.0000, 0.0909
testing/wikipedia/v3/04654.html
x
(
2
x
2
+
y
2
)
y
(
a
2
-
x
2
)
=
d
y
d
x
Doc 73
0.0909, -19.0000, 1.0000, 0.0909
testing/wikipedia/v3/07344.html
d
s
2
=
4
(
d
x
2
+
d
y
2
)
(
1
-
x
2
-
y
2
)
2
.
Doc 74
0.0909, -21.0000, 2.0000, 0.0909
testing/wikipedia/v3/21607.html
f
y
=
y
0
-
y
(
x
0
-
x
)
2
+
(
y
0
-
y
)
2
(
20
)
Doc 56
0.1297, -17.0000, 3.0000, 0.2206
testing/wikipedia/v3/23312.html