tangent
Not Supported
p
=
-
x
±
x
x0
-
4
(
x1
)
(
x2
x3
-
y
)
2
(
-
g
x
2
x4
)
Search
Returned 94 matches (100 formulae, 77 docs)
Lookup 110.093 ms, Re-ranking 2855.703 ms
Found 462310 tuple postings, 111072 formulae, 18422 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, 1.5963
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
Z
P
=
b
h
2
4
-
(
b
-
2
t
)
(
h
2
-
t
)
2
Doc 5
0.2821, -13.0000, 4.0000, 0.2821
testing/wikipedia/v3/21772.html
p
=
v
2
±
v
4
-
g
(
g
x
2
+
2
y
v
2
)
g
x
Doc 1
0.9245, -16.0000, 22.0000, 1.5963
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 6
0.2595, -26.0000, 4.0000, 0.3892
testing/wikipedia/v3/02322.html
β
^
=
(
1
-
x
¯
)
(
x
¯
(
1
-
x
¯
)
v
¯
-
1
)
,
Doc 7
0.2442, -15.0000, 4.0000, 0.2442
testing/wikipedia/v3/02956.html
=
(
3
331
)
(
5
331
)
(
161
331
)
Doc 8
0.2062, -7.0000, 3.0000, 0.6186
testing/wikipedia/v3/00617.html
=
(
3
331
)
(
5
331
)
(
823
331
)
Doc 8
0.2062, -7.0000, 3.0000, 0.6186
testing/wikipedia/v3/00617.html
(
a
m
n
)
=
(
a
m
)
(
a
n
)
Doc 10
0.2062, -8.0000, 3.0000, 0.4124
testing/wikipedia/v3/02166.html
(
a
n
m
)
=
(
a
n
)
(
a
m
)
Doc 9
0.2062, -8.0000, 3.0000, 0.4124
testing/wikipedia/v3/06302.html
(
a
b
n
)
=
(
a
n
)
(
b
n
)
Doc 9
0.2062, -8.0000, 3.0000, 0.4124
testing/wikipedia/v3/06302.html
Doc 10
0.2062, -8.0000, 3.0000, 0.4124
testing/wikipedia/v3/02166.html
(
a
b
p
)
=
(
a
p
)
(
b
p
)
.
Doc 8
0.2062, -7.0000, 3.0000, 0.6186
testing/wikipedia/v3/00617.html
(
v
c
)
2
(
r
r
s
-
1
)
=
1
2
.
Doc 11
0.2062, -11.0000, 4.0000, 0.3359
testing/wikipedia/v3/02950.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, 1.5963
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, 1.5963
testing/wikipedia/v3/09833.html
ϕ
1
(
v
)
=
(
1
)
(
1
6
)
=
1
6
Doc 12
0.1818, -9.0000, 3.0000, 0.1818
testing/wikipedia/v3/02868.html
x
(
t
)
=
2
(
t
a
-
⌊
1
2
+
t
a
⌋
)
Doc 13
0.1818, -13.0000, 4.0000, 0.3499
testing/wikipedia/v3/01650.html
f
(
y
)
=
1
y
2
-
x
Doc 14
0.1681, -5.0000, 2.0000, 0.1681
testing/wikipedia/v3/23526.html
cos
(
arccsc
x
)
=
x
2
-
1
x
Doc 15
0.1681, -7.0000, 3.0000, 0.5042
testing/wikipedia/v3/04392.html
sin
(
arcsec
x
)
=
x
2
-
1
x
Doc 15
0.1681, -7.0000, 3.0000, 0.5042
testing/wikipedia/v3/04392.html
(
arcosh
x
)
′
=
1
x
2
-
1
Doc 16
0.1681, -7.0000, 3.0000, 0.3361
testing/wikipedia/v3/16716.html
tan
(
arccsc
x
)
=
1
x
2
-
1
Doc 15
0.1681, -7.0000, 3.0000, 0.5042
testing/wikipedia/v3/04392.html
(
arcsec
x
)
′
=
1
|
x
|
x
2
-
1
Doc 16
0.1681, -7.0000, 3.0000, 0.3361
testing/wikipedia/v3/16716.html
r
1
2
=
-
p
2
=
-
b
2
a
Doc 17
0.1681, -10.0000, 4.0000, 0.1681
testing/wikipedia/v3/01801.html
h
(
t
)
=
1
2
j
ψ
(
-
t
2
j
)
Doc 18
0.1681, -11.0000, 3.0000, 0.1681
testing/wikipedia/v3/06756.html
=
2
(
t
a
-
floor
(
1
2
+
t
a
)
)
Doc 13
0.1818, -13.0000, 4.0000, 0.3499
testing/wikipedia/v3/01650.html
x
(
t
)
=
|
2
(
t
a
-
⌊
t
a
+
1
2
⌋
)
|
Doc 19
0.1681, -15.0000, 3.0000, 0.1681
testing/wikipedia/v3/01651.html
l
n
(
1
-
x
)
=
-
x
-
x
2
2
-
x
3
3
-
…
Doc 20
0.1681, -16.0000, 2.0000, 0.1681
testing/wikipedia/v3/25151.html
M
x
=
(
-
x
4
2
+
4
x
3
3
-
20
x
2
+
80
x
)
|
0
2
Doc 21
0.1681, -20.0000, 3.0000, 0.1681
testing/wikipedia/v3/11687.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 23
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 22
0.1681, -21.0000, 3.0000, 0.2978
testing/wikipedia/v3/27724.html
1
(
u
+
A
)
(
u
-
A
)
=
1
2
A
(
1
u
-
A
-
1
u
+
A
)
Doc 24
0.1681, -22.0000, 3.0000, 0.1681
testing/wikipedia/v3/05353.html
q
2
g
(
1
y
1
-
1
y
2
)
=
1
2
(
y
z
2
-
y
1
2
)
.
Doc 25
0.1681, -22.0000, 3.0000, 0.1681
testing/wikipedia/v3/27176.html
=
1
2
m
3
x
˙
2
+
1
2
M
v
2
-
1
2
k
x
2
-
m
g
x
2
-
M
g
x
Doc 26
0.1681, -28.0000, 2.0000, 0.1681
testing/wikipedia/v3/23806.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 27
0.1681, -29.0000, 3.0000, 0.2978
testing/wikipedia/v3/09923.html
s
x
y
=
1
N
∑
n
=
1
N
(
x
n
-
x
¯
)
(
y
n
-
y
¯
)
.
Doc 28
0.1519, -19.0000, 4.0000, 0.1519
testing/wikipedia/v3/17362.html
Cov
(
X
,
Y
)
=
∑
i
=
1
n
(
x
i
-
x
¯
)
(
y
i
-
y
¯
)
n
.
Doc 29
0.1519, -20.0000, 4.0000, 0.1519
testing/wikipedia/v3/00018.html
r
x
y
=
x
y
¯
-
x
¯
y
¯
(
x
2
¯
-
x
¯
2
)
(
y
2
¯
-
y
¯
2
)
Doc 30
0.1519, -20.0000, 4.0000, 0.1519
testing/wikipedia/v3/10770.html
f
(
x
;
k
)
=
2
1
-
k
2
x
k
-
1
e
-
x
2
2
Γ
(
k
2
)
Doc 31
0.1519, -22.0000, 5.0000, 0.1519
testing/wikipedia/v3/09559.html
(
x
3
-
y
2
N
)
=
1
Doc 32
0.1422, -5.0000, 3.0000, 0.2434
testing/wikipedia/v3/25162.html
f
(
x
)
=
1
π
(
x
-
a
)
(
b
-
x
)
Doc 33
0.1422, -11.0000, 3.0000, 0.1422
testing/wikipedia/v3/25332.html
d
y
d
x
=
-
4
x
3
4
y
=
-
x
3
y
Doc 34
0.1422, -14.0000, 3.0000, 0.1422
testing/wikipedia/v3/03420.html
P
4
2
(
x
)
=
15
2
(
7
x
2
-
1
)
(
1
-
x
2
)
Doc 35
0.1422, -16.0000, 3.0000, 0.1422
testing/wikipedia/v3/07434.html
λ
=
1
2
(
-
b
m
±
b
2
m
2
-
4
ω
0
2
)
.
Doc 36
0.1422, -18.0000, 3.0000, 0.1422
testing/wikipedia/v3/04432.html
G
=
n
(
n
-
1
)
(
n
-
2
)
∑
i
=
1
n
(
x
i
-
x
¯
s
)
3
Doc 37
0.1422, -21.0000, 2.0000, 0.1422
testing/wikipedia/v3/00967.html
q
x
y
=
∑
(
x
-
x
¯
)
(
y
-
y
¯
)
I
(
x
,
y
)
∑
I
(
x
,
y
)
Doc 38
0.1422, -22.0000, 4.0000, 0.1422
testing/wikipedia/v3/22368.html
F
(
x
)
=
Φ
(
x
-
μ
σ
)
=
1
2
[
1
+
erf
(
x
-
μ
σ
2
)
]
Doc 39
0.1422, -22.0000, 2.0000, 0.1422
testing/wikipedia/v3/00697.html
d
d
x
(
1
x
3
+
4
x
)
=
-
3
x
2
-
4
(
x
3
+
4
x
)
2
.
Doc 40
0.1422, -23.0000, 4.0000, 0.1422
testing/wikipedia/v3/13099.html
τ
x
y
=
μ
b
2
π
(
1
-
ν
)
x
(
x
2
-
y
2
)
(
x
2
+
y
2
)
2
Doc 41
0.1422, -23.0000, 3.0000, 0.2844
testing/wikipedia/v3/06599.html
σ
y
y
=
μ
b
2
π
(
1
-
ν
)
y
(
x
2
-
y
2
)
(
x
2
+
y
2
)
2
Doc 41
0.1422, -23.0000, 3.0000, 0.2844
testing/wikipedia/v3/06599.html
Q
(
x
)
=
1
2
-
1
2
erf
(
x
2
)
=
1
2
erfc
(
x
2
)
.
Doc 42
0.1422, -23.0000, 3.0000, 0.1422
testing/wikipedia/v3/02688.html
4
⋅
∫
0
1
(
x
2
-
x
6
)
1
6
d
x
=
Γ
(
1
6
)
⋅
Γ
(
1
3
)
3
π
≈
2.804
,
Doc 43
0.1422, -30.0000, 2.0000, 0.1422
testing/wikipedia/v3/13906.html
z
=
x
2
-
y
2
2
.
Doc 6
0.2595, -26.0000, 4.0000, 0.3892
testing/wikipedia/v3/02322.html
f
(
x
)
=
1
x
3
-
1
Doc 44
0.1297, -6.0000, 2.0000, 0.3892
testing/wikipedia/v3/03370.html
f
(
x
)
=
1
x
2
-
1
Doc 45
0.1297, -6.0000, 2.0000, 0.1297
testing/wikipedia/v3/03892.html
=
-
x
-
x
2
2
-
x
3
6
Doc 46
0.1297, -9.0000, 2.0000, 0.2595
testing/wikipedia/v3/08705.html
ψ
1
(
3
2
)
=
π
2
2
-
4
Doc 47
0.1297, -9.0000, 2.0000, 0.1297
testing/wikipedia/v3/09858.html
f
(
x
)
=
1
x
sin
(
1
x
3
)
.
Doc 48
0.1297, -10.0000, 2.0000, 0.1297
testing/wikipedia/v3/04671.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
V
(
𝐫
)
=
-
μ
1
r
1
-
μ
2
r
2
Doc 50
0.1297, -12.0000, 3.0000, 0.1297
testing/wikipedia/v3/08655.html
w
=
F
6
E
I
(
3
L
x
2
-
x
3
)
.
Doc 27
0.1681, -29.0000, 3.0000, 0.2978
testing/wikipedia/v3/09923.html
d
r
=
|
x
-
y
|
(
|
x
+
y
|
2
)
.
Doc 53
0.1297, -12.0000, 2.0000, 0.1297
testing/wikipedia/v3/16672.html
1
6
(
-
x
3
+
9
x
2
-
18
x
+
6
)
Doc 51
0.1297, -12.0000, 2.0000, 0.1297
testing/wikipedia/v3/07059.html
|
q
|
=
4
π
n
λ
0
sin
(
θ
2
)
(
5
)
Doc 52
0.1297, -12.0000, 2.0000, 0.1297
testing/wikipedia/v3/18092.html
∂
φ
∂
t
=
∂
2
φ
∂
x
2
-
x
2
φ
Doc 54
0.1297, -13.0000, 2.0000, 0.1297
testing/wikipedia/v3/26570.html
f
(
x
)
=
x
3
+
16
x
3
-
4
x
2
+
8
x
Doc 44
0.1297, -6.0000, 2.0000, 0.3892
testing/wikipedia/v3/03370.html
ρ
t
(
x
)
=
1
2
π
t
e
-
x
2
2
t
,
Doc 55
0.1297, -15.0000, 4.0000, 0.1297
testing/wikipedia/v3/04918.html
f
(
x
)
=
x
x
4
+
10
x
2
-
96
x
-
71
,
Doc 56
0.1297, -15.0000, 2.0000, 0.1297
testing/wikipedia/v3/03663.html
r
r
s
(
v
c
)
2
(
1
-
r
s
r
)
=
1
2
Doc 11
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 46
0.1297, -9.0000, 2.0000, 0.2595
testing/wikipedia/v3/08705.html
f
(
x
)
=
1
+
2
(
1
x
+
x
x
2
-
4
x
+
8
)
Doc 44
0.1297, -6.0000, 2.0000, 0.3892
testing/wikipedia/v3/03370.html
a
2
=
2
x
-
2
x
-
2
x
2
-
2
x
+
3
2
Doc 57
0.1297, -17.0000, 2.0000, 0.1297
testing/wikipedia/v3/30289.html
y
=
R
(
2
(
x
L
)
-
K
′
(
x
L
)
2
2
-
K
′
)
Doc 58
0.1297, -18.0000, 3.0000, 0.1297
testing/wikipedia/v3/09114.html
=
1
θ
k
Γ
(
k
)
(
1
y
)
k
+
1
exp
(
-
1
θ
y
)
Doc 59
0.1297, -18.0000, 3.0000, 0.1297
testing/wikipedia/v3/09040.html
∂
w
∂
t
=
1
2
∂
2
w
∂
x
2
-
u
V
(
x
)
w
Doc 60
0.1297, -18.0000, 2.0000, 0.1297
testing/wikipedia/v3/05897.html
f
(
x
)
=
1
-
x
+
x
2
-
x
3
+
⋯
=
1
1
+
x
.
Doc 61
0.1297, -18.0000, 2.0000, 0.1297
testing/wikipedia/v3/16042.html
1
+
7
x
+
12
x
2
-
4
x
3
(
1
-
x
2
)
(
1
-
16
x
2
)
Doc 62
0.1297, -20.0000, 3.0000, 0.3323
testing/wikipedia/v3/24194.html
f
(
x
)
=
1
b
-
a
rect
(
x
-
(
a
+
b
2
)
b
-
a
)
.
Doc 63
0.1297, -20.0000, 2.0000, 0.1297
testing/wikipedia/v3/09125.html
f
(
x
)
=
1
2
∫
ℝ
n
(
x
-
y
|
x
-
y
|
+
y
|
y
|
)
d
μ
(
y
)
Doc 64
0.1297, -24.0000, 2.0000, 0.1297
testing/wikipedia/v3/26239.html
π
x
2
6
-
3
x
2
-
(
x
2
)
2
2
+
x
2
-
(
x
2
)
2
2
Doc 65
0.1297, -26.0000, 3.0000, 0.1297
testing/wikipedia/v3/00025.html
2
3
(
1
+
x
)
3
p
(
3
2
+
2
x
1
+
x
)
=
8
x
3
+
4
x
2
-
4
x
-
1
Doc 22
0.1681, -21.0000, 3.0000, 0.2978
testing/wikipedia/v3/27724.html
v
a
r
[
log
(
t
a
)
]
=
(
s
a
2
t
a
2
+
(
x
a
-
x
¯
t
a
)
2
-
1
)
n
Doc 66
0.1297, -28.0000, 2.0000, 0.1297
testing/wikipedia/v3/00627.html
V
=
m
2
(
g
L
a
x
a
2
+
g
L
b
x
b
2
+
k
m
(
x
b
-
x
a
)
2
)
.
Doc 67
0.1297, -29.0000, 3.0000, 0.1297
testing/wikipedia/v3/08199.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
m
=
x
3
-
y
2
x
(
mod
N
)
Doc 32
0.1422, -5.0000, 3.0000, 0.2434
testing/wikipedia/v3/25162.html
1
+
3
x
(
1
-
x
2
)
(
1
-
4
x
)
Doc 62
0.1297, -20.0000, 3.0000, 0.3323
testing/wikipedia/v3/24194.html
1
+
7
x
(
1
-
x
2
)
(
1
-
16
x
2
)
Doc 62
0.1297, -20.0000, 3.0000, 0.3323
testing/wikipedia/v3/24194.html
p
=
x
3
-
y
3
x
-
y
(
x
=
y
+
1
)
.
Doc 69
0.1013, -14.0000, 1.0000, 0.1013
testing/wikipedia/v3/04515.html
v
=
x
-
x
¯
h
(
x
)
;
w
=
y
-
y
¯
h
(
y
)
Doc 70
0.1013, -17.0000, 3.0000, 0.1922
testing/wikipedia/v3/09762.html
G
(
P
(
n
)
;
x
)
=
3
-
x
2
1
-
x
2
-
x
3
.
Doc 71
0.1013, -17.0000, 3.0000, 0.1013
testing/wikipedia/v3/26388.html
z
=
x
-
x
¯
h
Doc 70
0.1013, -17.0000, 3.0000, 0.1922
testing/wikipedia/v3/09762.html
Z
=
Y
y
(
1
-
x
-
y
)
Doc 72
0.0909, -8.0000, 2.0000, 0.0909
testing/wikipedia/v3/10026.html
δ
(
x
)
=
x
-
x
p
p
.
Doc 73
0.0909, -8.0000, 1.0000, 0.0909
testing/wikipedia/v3/25318.html
s
(
x
)
=
x
1
-
x
-
x
2
Doc 74
0.0909, -9.0000, 2.0000, 0.0909
testing/wikipedia/v3/00385.html
G
(
P
(
n
)
;
x
)
=
1
+
x
1
-
x
2
-
x
3
.
Doc 75
0.0909, -17.0000, 2.0000, 0.0909
testing/wikipedia/v3/10108.html
(
ℱ
g
)
(
y
)
=
1
ε
n
e
-
π
ε
2
|
x
-
y
|
2
.
Doc 76
0.0909, -19.0000, 2.0000, 0.0909
testing/wikipedia/v3/04443.html
d
s
2
=
4
(
d
x
2
+
d
y
2
)
(
1
-
x
2
-
y
2
)
2
.
Doc 77
0.0909, -21.0000, 2.0000, 0.0909
testing/wikipedia/v3/21607.html