This document contains formulas and definitions related to calculus and trigonometry. It includes: 1) Formulas for addition, subtraction, multiplication, and exponentiation of variables. 2) Definitions of trigonometric functions like sine, cosine, and tangent. It also includes their inverses and various trigonometric identities. 3) Formulas for sums, products, and limits involving variables. 4) Definitions of hyperbolic functions like sinh, cosh, and tanh and their inverses.

1. Fórmulas de Cálculo Diferencial e Integral (Página 1 de 3) http://www.geocities.com/calculusjrm/ Jesús Rubí M.
Fórmulas de ( a + b ) ⋅ ( a − ab + b ) = a + b
2 2 3 3 Gráfica 4. Las funciones trigonométricas inversas
arcctg x , arcsec x , arccsc x : sin α + sin β = 2sin
1 1
(α + β ) ⋅ cos (α − β )
( a + b ) ⋅ ( a3 − a 2 b + ab 2 − b3 ) = a 4 − b 4
2 2
Cálculo Diferencial HIP
CO 4 1 1
sin α − sin β = 2 sin (α − β ) ⋅ cos (α + β )
( a + b ) ⋅ ( a 4 − a 3b + a 2 b 2 − ab3 + b 4 ) = a 5 + b5
e Integral ACTUALIZADO AGO-2007 θ 3
2 2
( a + b ) ⋅ ( a5 − a 4 b + a 3b 2 − a 2 b3 + ab 4 − b5 ) = a 6 − b 6
1 1
CA cos α + cos β = 2 cos (α + β ) ⋅ cos (α − β )
Jesús Rubí Miranda (jesusrubim@yahoo.com) 2 2 2
Móvil. Méx. DF. 044 55 13 78 51 94 1 1
⎛ ⎞ cos α − cos β = −2 sin (α + β ) ⋅ sin (α − β )
n
( a + b ) ⋅ ⎜ ∑ ( −1)
k +1
a n − k b k −1 ⎟ = a n + b n ∀ n ∈ impar θ sin cos tg ctg sec csc
1
2 2
⎝ k =1 ⎠
1. VALOR ABSOLUTO 0 0 1 0 ∞ 1 ∞
sin (α ± β )
0
⎛ n
⎞ tg α ± tg β =
( a + b ) ⋅ ⎜ ∑ ( −1)
k +1 12
⎧a si a ≥ 0 a n − k b k −1 ⎟ = a n − b n ∀ n ∈ par 30 3 2 1 3 3 2 3 2
a =⎨ ⎝ k =1 ⎠
-1
arc ctg x cos α ⋅ cos β
45 1 2 1 2 2 2
⎩− a si a < 0
1 1 arc sec x
arc csc x
1
⎡sin (α − β ) + sin (α + β ) ⎤
5. SUMAS Y PRODUCTOS 60 3 2 12 3 1 3 2 2 3 -2
sin α ⋅ cos β =
a = −a 2⎣ ⎦
-5 0 5
∞ ∞
n
+ a n = ∑ ak
90 1 0 0 1
a ≤ a y −a ≤ a a1 + a2 + 8. IDENTIDADES TRIGONOMÉTRICAS 1
k =1 ⎡ π π⎤ sin α ⋅ sin β = ⎡cos (α − β ) − cos (α + β ) ⎤
sin θ + cos 2 θ = 1 2⎣ ⎦
2
a ≥0 y a =0 ⇔ a=0 n y = ∠ sin x y ∈ ⎢− , ⎥
∑ c = nc ⎣ 2 2⎦
1 + ctg 2 θ = csc 2 θ
cos α ⋅ cos β =
1
⎡cos (α − β ) + cos (α + β ) ⎤
y = ∠ cos x y ∈ [ 0, π ]
n n
∏a = ∏ ak 2⎣ ⎦
k =1
ab = a b ó k n n tg 2 θ + 1 = sec 2 θ
k =1 k =1
∑ ca = c ∑ ak
y = ∠ tg x y∈ −
π π tg α + tg β
sin ( −θ ) = − sin θ
k
n n k =1 k =1
, tg α ⋅ tg β =
a+b ≤ a + b ó ∑a ≤ ∑ ak n n n
2 2 ctg α + ctg β
cos ( −θ ) = cos θ
k
k =1 k =1
∑(a k + bk ) = ∑ ak + ∑ bk
y = ∠ ctg x = ∠ tg
1
y ∈ 0, π 9. FUNCIONES HIPERBÓLICAS
tg ( −θ ) = − tg θ
k =1 k =1 k =1
2. EXPONENTES x ex − e− x
sinh x =
n
a p ⋅ a q = a p+q ∑(a
k =1
k − ak −1 ) = an − a0 y = ∠ sec x = ∠ cos
1
y ∈ [ 0, π ] sin (θ + 2π ) = sin θ 2
ap x
= a p−q e x + e− x
n
n 1 ⎡ π π⎤ cos (θ + 2π ) = cos θ cosh x =
aq
∑ ⎡ a + ( k − 1) d ⎤ = 2 ⎡ 2a + ( n − 1) d ⎤
⎣ ⎦ ⎣ ⎦ y = ∠ csc x = ∠ sen y ∈ ⎢− , ⎥
⎣ 2 2⎦ tg (θ + 2π ) = tg θ
2
(a )
p q
=a pq k =1 x
tgh x =
sinh x e x − e − x
=
n
(a + l ) Gráfica 1. Las funciones trigonométricas: sin x , sin (θ + π ) = − sin θ cosh x e x + e− x
(a ⋅b) = a ⋅b =
p p p
2 cos x , tg x : cos (θ + π ) = − cos θ 1 e x + e− x
p n
1 − r n a − rl ctgh x = =
⎛a⎞ ap
⎜ ⎟ = p ∑ ar k −1 = a 1 − r = 1 − r 2 tg (θ + π ) = tg θ tgh x e x − e − x
⎝b⎠ b k =1
1 2
sin (θ + nπ ) = ( −1) sin θ sech x = =
1.5 n
∑ k = 2 ( n2 + n )
n
a = a 1
cosh x e x + e − x
p/q q p
1
cos (θ + nπ ) = ( −1) cos θ
n
3. LOGARITMOS k =1 1 2
n ( n + 1)( 2n + 1)
0.5
csch x = =
∑ k 2 = 6 ( 2n3 + 3n2 + n ) = tg (θ + nπ ) = tg θ sinh x e x − e − x
n
log a N = x ⇒ a x = N 1
0
log a MN = log a M + log a N k =1 6 sinh : →
-0.5
sin ( nπ ) = 0
∑ k = 4 ( n + 2n + n ) → [1, ∞
n
M 3 1 4 3 2 cosh :
= log a M − log a N cos ( nπ ) = ( −1)
-1
n
log a k =1
N -1.5 sen x
tgh : → −1,1
tg ( nπ ) = 0
cos x
∑ k 4 = 30 ( 6n5 + 15n4 + 10n3 − n )
n
log a N = r log a N
r 1
− {0} → −∞ , −1 ∪ 1, ∞
tg x
-2
-8 -6 -4 -2 0 2 4 6 8 ctgh :
k =1
⎛ 2n + 1 ⎞
π ⎟ = ( −1)
log b N ln N
→ 0 ,1]
n
log a N = = 1+ 3 + 5 + + ( 2n − 1) = n 2 Gráfica 2. Las funciones trigonométricas csc x , sin ⎜ sech :
log b a ln a ⎝ 2 ⎠
sec x , ctg x : csch : − {0} → − {0}
⎛ 2n + 1 ⎞
n
log10 N = log N y log e N = ln N n! = ∏ k cos ⎜ π⎟=0
4. ALGUNOS PRODUCTOS k =1 2.5 ⎝ 2 ⎠ Gráfica 5. Las funciones hiperbólicas sinh x ,
a ⋅ ( c + d ) = ac + ad ⎛n⎞ n! 2
⎛ 2n + 1 ⎞ cosh x , tgh x :
⎜ ⎟= , k≤n tg ⎜ π⎟=∞
⎝ k ⎠ ( n − k ) !k !
1.5
( a + b ) ⋅ ( a − b ) = a 2 − b2 1
⎝ 2 ⎠ 5
4
n
⎛n⎞ ⎛ π⎞
( a + b ) ⋅ ( a + b ) = ( a + b ) = a 2 + 2ab + b 2 ( x + y ) = ∑ ⎜ ⎟ x n −k y k
2 n 0.5
sin θ = cos ⎜ θ − ⎟ 3
k =0 ⎝ k ⎠ ⎝ 2⎠
0
( a − b ) ⋅ ( a − b ) = ( a − b ) = a 2 − 2ab + b 2
2
2
-0.5
⎛ π⎞ 1
( x1 + x2 + + xk ) = ∑
n! cos θ = sin ⎜ θ + ⎟
( x + b ) ⋅ ( x + d ) = x 2 + ( b + d ) x + bd x1n1 ⋅ x2 2
n -1
n
xknk
⎝ 2⎠ 0
n1 ! n2 ! nk ! -1.5
( ax + b ) ⋅ ( cx + d ) = acx 2 + ( ad + bc ) x + bd
csc x -1
sin (α ± β ) = sin α cos β ± cos α sin β
-2 sec x
6. CONSTANTES ctg x -2
( a + b ) ⋅ ( c + d ) = ac + ad + bc + bd
-2.5
π = 3.14159265359… cos (α ± β ) = cos α cos β ∓ sin α sin β
-8 -6 -4 -2 0 2 4 6 8 senh x
-3 cosh x
tgh x
( a + b ) = a3 + 3a 2b + 3ab 2 + b3 e = 2.71828182846…
3 -4
Gráfica 3. Las funciones trigonométricas inversas tg α ± tg β -5 0 5
tg (α ± β ) = 10. FUNCIONES HIPERBÓLICAS INV
( a − b ) = a 3 − 3a 2b + 3ab 2 − b3
3 7. TRIGONOMETRÍA arcsin x , arccos x , arctg x : 1 ∓ tg α tg β
( a + b + c ) = a 2 + b 2 + c 2 + 2ab + 2ac + 2bc
2 sen θ =
CO
cscθ =
1 4 sin 2θ = 2sin θ cos θ (
sinh −1 x = ln x + x 2 + 1 , ∀x ∈ )
sen θ
( )
HIP
cos 2θ = cos θ − sin θ
2 2
cosh −1 x = ln x ± x 2 − 1 , x ≥ 1
( a − b ) ⋅ ( a 2 + ab + b 2 ) = a 3 − b3
3
CA 1
cosθ = secθ = 2 tg θ
HIP cosθ tg 2θ = 1 ⎛1+ x ⎞
( a − b ) ⋅ ( a 3 + a 2 b + ab 2 + b3 ) = a 4 − b 4 1 − tg 2 θ
2
sen θ CO 1 tgh −1 x = ln ⎜ ⎟, x <1
tgθ = = ctgθ = 2 ⎝1− x ⎠
( a − b ) ⋅ ( a 4 + a 3b + a 2 b 2 + ab3 + b 4 ) = a 5 − b5 cosθ CA tgθ 1
sin 2 θ = (1 − cos 2θ )
1
1 ⎛ x +1⎞
0
2 ctgh −1 x = ln ⎜ ⎟, x >1
⎛ n
⎞ 2 ⎝ x −1⎠
( a − b ) ⋅ ⎜ ∑ a n − k b k −1 ⎟ = a n − b n ∀n ∈ π radianes=180 1
cos 2 θ = (1 + cos 2θ )
⎝ k =1 ⎠ -1
arc sen x
2 ⎛ 1 ± 1 − x2 ⎞
sech −1 x = ln ⎜ ⎟, 0 < x ≤ 1
arc cos x
arc tg x
1 − cos 2θ ⎜ ⎟
-2
-3 -2 -1 0 1 2 3 tg 2 θ = ⎝ x ⎠
1 + cos 2θ
⎛1 x2 + 1 ⎞
csch −1 x = ln ⎜ + ⎟, x ≠ 0
⎜x x ⎟
⎝ ⎠

2. Fórmulas de Cálculo Diferencial e Integral (Página 2 de 3) http://www.geocities.com/calculusjrm/ Jesús Rubí M.
∫ tgh udu = ln cosh u
11. IDENTIDADES DE FUNCS HIP d dv du 18. DERIVADA DE FUNCS HIPERBÓLICAS 22. INTEGRALES DE FUNCS LOG & EXP
( uv ) = u + v
cosh 2 x − sinh 2 x = 1 d du
∫ e du = e
u u
dx dx dx sinh u = cosh u
1 − tgh x = sech x d dw dv du dx dx ∫ ctgh udu = ln sinh u
( uvw ) = uv + uw + vw
2 2
au ⎧a > 0
∫ a du = ln a ⎨a ≠ 1 ∫ sech udu = ∠ tg ( sinh u )
u
dx dx dx dx d du
ctgh 2 x − 1 = csch 2 x cosh u = sinh u
⎩
d ⎛ u ⎞ v ( du dx ) − u ( dv dx ) dx dx
sinh ( − x ) = − sinh x ∫ csch udu = − ctgh ( cosh u )
−1
⎜ ⎟= d du au ⎛ 1 ⎞
dx ⎝ v ⎠ ∫ ua du = ln a ⋅ ⎜ u − ln a ⎟
2
tgh u = sech 2 u
u
v
cosh ( − x ) = cosh x dx dx ⎝ ⎠ 1
= ln tgh u
tgh ( − x ) = − tgh x
d n
dx
( u ) = nu n−1 du
dx
d
ctgh u = − csch 2 u
du
∫ ue du = e ( u − 1)
u u 2
dx dx 26. INTEGRALES DE FRAC
sinh ( x ± y ) = sinh x cosh y ± cosh x sinh y dF dF du ∫ ln udu =u ln u − u = u ( ln u − 1)
= ⋅ (Regla de la Cadena) d
sech u = − sech u tgh u
du du 1 u
cosh ( x ± y ) = cosh x cosh y ± sinh x sinh y dx du dx dx dx 1 u ∫ u 2 + a 2 = a ∠ tg a
du 1 ∫ log udu =( u ln u − u ) = ( ln u − 1)
tgh x ± tgh y
a
= d du ln a ln a
tgh ( x ± y ) = csch u = − csch u ctgh u 1 u
dx dx du = − ∠ ctg
1 ± tgh x tgh y
2
dx dx u
∫ u log a udu = 4 ⋅ ( 2log a u − 1)
a a
dF dF du 1 u−a
sinh 2 x = 2sinh x cosh x 19. DERIVADA DE FUNCS HIP INV
=
∫ u 2 − a 2 = 2a ln u + a ( u > a )
du 2 2
dx dx du d 1 du u 2
cosh 2 x = cosh 2 x + sinh 2 x
dy dy dt f 2′ ( t ) ⎪ x = f1 ( t )
⎧
senh −1 u = ⋅
1 + u 2 dx ∫ u ln udu = 4 ( 2ln u − 1) 1 a+u
∫ a 2 − u 2 = 2a ln a − u ( u < a )
dx du 2 2
tgh 2 x =
2 tgh x = = donde ⎨
1 + tgh 2 x dx dx dt f1′( t ) ⎪ y = f2 (t )
⎩ d ±1 du ⎧+ si cosh -1u > 0
⎪ 23. INTEGRALES DE FUNCS TRIGO
cosh −1 u = ⋅ , u >1 ⎨
1 15. DERIVADA DE FUNCS LOG & EXP dx u 2 − 1 dx ⎪− si cosh u < 0
⎩
-1
∫ sin udu = − cos u 27. INTEGRALES CON RAIZ
sinh 2 x = ( cosh 2 x − 1) du
∫ a 2 − u 2 = ∠ sin a
u
2 d
( ln u ) =
du dx 1 du
= ⋅
d
tgh −1 u =
1 du
⋅ , u <1 ∫ cos udu = sin u
1 dx u u dx dx 1 − u 2 dx
cosh x = ( cosh 2 x + 1) ∫ sec udu = tg u
2 2
u
d log e du d 1 du = −∠ cos
2 ( log u ) = ⋅ ctgh −1 u = ⋅ , u >1 a
cosh 2 x − 1 1 − u 2 dx ∫ csc udu = − ctg u
2
dx u dx dx
tgh 2 x =
cosh 2 x + 1 d log e du
( log a u ) = a ⋅ a > 0, a ≠ 1 d
sech −1 u =
∓1
⋅ ⎨
⎧− −1
du ⎪ si sech u > 0, u ∈ 0,1
∫ sec u tg udu = sec u ∫
du
u 2 ± a2
(
= ln u + u 2 ± a 2 )
dx u dx −1
tgh x =
sinh 2 x dx u 1 − u 2 dx ⎪ + si sech u < 0, u ∈ 0,1
⎩
cosh 2 x + 1
d u
( e ) = eu ⋅ du d −1 1 du ∫ csc u ctg udu = − csc u ∫u
du 1
ln =
u
dx dx csch u = − ⋅ , u≠0 a2 ± u 2
a a + a2 ± u 2
e x = cosh x + sinh x dx u 1 + u 2 dx ∫ tg udu = − ln cos u = ln sec u
e − x = cosh x − sinh x
d u
( a ) = au ln a ⋅ du du 1 a
∫ u u 2 − a 2 = a ∠ cos u
dx dx 20. INTEGRALES DEFINIDAS, PROPIEDADES ∫ ctg udu = ln sin u
12. OTRAS
ax 2 + bx + c = 0
d v
dx
( u ) = vu v−1 du + ln u ⋅ u v ⋅ dv
dx dx
Nota. Para todas las fórmulas de integración deberá
agregarse una constante arbitraria c (constante de ∫ sec udu = ln sec u + tg u 1
= ∠ sec
u
a a
⇒ x=
−b ± b 2 − 4ac
16. DERIVADA DE FUNCIONES TRIGO integración).
∫ csc udu = ln csc u − ctg u u 2 a2 u
∫ { f ( x ) ± g ( x )} dx = ∫ f ( x ) dx ± ∫ g ( x ) dx ∫ a − u du = 2 a − u + 2 ∠ sen a
b b b 2 2 2
d du
2a ( sin u ) = cos u u 1
∫ sin udu =
− sin 2u
a a a 2
dx dx
b 2 − 4ac = discriminante
∫ cf ( x ) dx = c ⋅ ∫ f ( x ) dx c ∈ ( )
b b 2
2 4 u 2 a
∫ u ± a du = 2 u ± a ± 2 ln u + u ± a
2 2 2 2 2
d du
exp (α ± i β ) = e α
( cos β ± i sin β ) si α , β ∈ ( cos u ) = − sin u a a
u 1
∫ cos udu = 2 + 4 sin 2u
2
dx dx
∫ f ( x ) dx = ∫ f ( x ) dx + ∫ f ( x ) dx
b c b
13. LÍMITES 28. MÁS INTEGRALES
d du
( tg u ) = sec2 u
a a c
∫ tg udu = tg u − u
2
e au ( a sin bu − b cos bu )
∫ f ( x ) dx = − ∫ f ( x ) dx
1 b a
lim (1 + x ) x = e = 2.71828... dx dx
∫e sin bu du =
au
a 2 + b2
∫ ctg udu = − ( ctg u + u )
x →0 a b
d du
( ctg u ) = − csc2 u
2
∫ f ( x ) dx = 0 e au ( a cos bu + b sin bu )
x a
⎛ 1⎞ dx dx
lim ⎜1 + ⎟ = e ∫e cos bu du =
a au
x →∞
⎝ x⎠ d
( sec u ) = sec u tg u
du
m ⋅ ( b − a ) ≤ ∫ f ( x ) dx ≤ M ⋅ ( b − a )
b ∫ u sin udu = sin u − u cos u a2 + b2
sen x dx dx 1 1
∫ u cos udu = cos u + u sin u ∫ sec u du = 2 sec u tg u + 2 ln sec u + tg u
a
=1
3
⇔ m ≤ f ( x ) ≤ M ∀x ∈ [ a, b ] , m, M ∈
lim
x →0 d du
x
( csc u ) = − csc u ctg u 24. INTEGRALES DE FUNCS TRIGO INV
1 − cos x dx dx 29. ALGUNAS SERIES
∫ f ( x ) dx ≤ ∫ g ( x ) dx
b b
lim =0
∫ ∠ sin udu = u∠ sin u + 1 − u f '' ( x0 )( x − x0 )
2 2
x →0 d du
( vers u ) = sen u
a a
x
ex −1 dx dx ⇔ f ( x ) ≤ g ( x ) ∀x ∈ [ a , b ] f ( x ) = f ( x0 ) + f ' ( x0 )( x − x0 ) +
=1 ∫ ∠ cos udu = u∠ cos u − 1 − u 2!
2
lim
∫ f ( x ) dx ≤ ∫ f ( x ) dx si a < b
17. DERIV DE FUNCS TRIGO INVER b b
f ( n ) ( x0 )( x − x0 )
x →0 x n
x −1 ∫ ∠ tg udu = u∠ tg u − ln 1 + u + +
a a 2
d 1 du : Taylor
lim =1 ( ∠ sin u ) = ⋅ 21. INTEGRALES n!
x →1 ln x dx 1 − u 2 dx f '' ( 0 ) x 2
∫ ∠ ctg udu = u∠ ctg u + ln 1 + u
2
14. DERIVADAS d 1 du ∫ adx =ax f ( x ) = f (0) + f ' ( 0) x +
( ∠ cos u ) = −
∫ ∠ sec udu = u∠ sec u − ln ( u + u )
⋅
f ( x + ∆x ) − f ( x )
2!
∆y 2
−1
∫ af ( x ) dx = a ∫ f ( x ) dx
df 1 − u 2 dx
Dx f ( x ) = = lim = lim dx
f ( n) ( 0 ) x n
dx ∆x →0 ∆x ∆x → 0 ∆x
+ + : Maclaurin
d
( ∠ tg u ) =
1 du = u∠ sec u − ∠ cosh u
d ⋅
∫ ( u ± v ± w ± ) dx = ∫ udx ± ∫ vdx ± ∫ wdx ± n!
∫ ∠ csc udu = u∠ csc u + ln ( u + )
(c) = 0 dx 1 + u 2 dx
u2 − 1 x 2 x3 xn
∫ udv = uv − ∫ vdu ( Integración por partes ) ex = 1 + x + + + + +
dx d 1 du
d ( ∠ ctg u ) = − ⋅ 2! 3! n!
( cx ) = c dx 1 + u 2 dx
u n +1
= u∠ csc u + ∠ cosh u 3 5 7
x 2 n −1
∫ u du = n + 1
x x x
n ≠ −1 + + ( −1)
dx n n −1
d 1 du ⎧+ si u > 1 25. INTEGRALES DE FUNCS HIP sin x = x − + −
( ∠ sec u ) = ± ⋅ ⎨ ( 2n − 1)!
( cx n ) = ncx n−1
d 3! 5! 7!
dx u u 2 − 1 dx ⎩− si u < −1 du ∫ sinh udu = cosh u
dx
du ⎧− si u > 1 ∫u = ln u
cos x = 1 −
x2 x4 x6
+ − + + ( −1)
n −1 x 2 n− 2
d du dv dw
(u ± v ± w ± ) = ± ± ±
d
( ∠ csc u ) = ∓
1
⋅ ⎨ ∫ cosh udu = sinh u 2! 4! 6! ( 2n − 2 ) !
dx dx dx dx dx u u 2 − 1 dx ⎩+ si u < −1
∫ sech udu = tgh u
2
x2 x3 x 4 n −1 x
n
d du d 1 du ln (1 + x ) = x −
+ − + + ( −1)
( cu ) = c ( ∠ vers u ) = ⋅
∫ csch udu = − ctgh u
2 2 3 4 n
dx dx dx 2u − u 2 dx 2 n −1
x3 x 5 x 7 n −1 x
∠ tg x = x − + − + + ( −1)
∫ sech u tgh udu = − sech u 3 5 7 2n − 1
∫ csch u ctgh udu = − csch u

3. Fórmulas de Cálculo Diferencial e Integral (Página 3 de 3) http://www.geocities.com/calculusjrm/ Jesús Rubí M.
30. ALFABETO GRIEGO
Mayúscula Minúscula Nombre Equivalente
Romano
1 Α α Alfa A
2 Β β Beta B
3 Γ γ Gamma G
4 ∆ δ Delta D
5 Ε ε Epsilon E
6 Ζ ζ Zeta Z
7 Η η Eta H
8 Θ θ ϑ Teta Q
9 Ι ι Iota I
10 Κ κ Kappa K
11 Λ λ Lambda L
12 Μ µ Mu M
13 Ν ν Nu N
14 Ξ ξ Xi X
15 Ο ο Omicron O
16 Π π ϖ Pi P
17 Ρ ρ Rho R
18 Σ σ ς Sigma S
19 Τ τ Tau T
20 Υ υ Ipsilon U
21 Φ φ ϕ Phi F
22 Χ χ Ji C
23 Ψ ψ Psi Y
24 Ω ω Omega W
31. NOTACIÓN
sin Seno.
cos Coseno.
tg Tangente.
sec Secante.
csc Cosecante.
ctg Cotangente.
vers Verso seno.
arcsin θ = sin θ Arco seno de un ángulo θ .
u = f ( x)
sinh Seno hiperbólico.
cosh Coseno hiperbólico.
tgh Tangente hiperbólica.
ctgh Cotangente hiperbólica.
sech Secante hiperbólica.
csch Cosecante hiperbólica.
u, v, w Funciones de x , u = u ( x ) , v = v ( x ) .
Conjunto de los números reales.
= {…, −2, −1,0,1, 2,…} Conjunto de enteros.
Conjunto de números racionales.
c
Conjunto de números irracionales.
= {1, 2,3,…} Conjunto de números naturales.
Conjunto de números complejos.