Tabla matemática 2

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TABLA MATEMÁTICA PROFESOR JOEL AMAURIS GELABERT S.
Funciones Trigonométricas de 30
0
45
0
60
0 Análisis combinatorio.
Vm,n = m (m-1)(m-2)…(m-n+1)
&#3627408386;
&#3627408422;,&#3627408423;=
&#3627408422;!
&#3627408423;! (&#3627408422;−&#3627408423;)!

Pm = m!
??????
&#3627408422;,&#3627408423;
,
= &#3627408422;
&#3627408423;

Sen 30
0 =
&#3627409359;
&#3627409360;

Cos 30
0 =
√&#3627409361;
&#3627409360;

Tan 30
0 =
√&#3627409361;
&#3627409361;

Cot 30
0 = √&#3627409361;

Sec 30
0 =
&#3627409360;√&#3627409361;
&#3627409361;

Cosc 30
0 = 2

Sen 45
0 =
√&#3627409360;
&#3627409360;

Cos 45
0 =
√&#3627409360;
&#3627409360;

Tan 45
0 =1

Cot 45
0 =1

Sec 45
0 = √&#3627409360;

Cosc 45
0 = √&#3627409360;
Sen 60
0 =
√&#3627409361;
&#3627409360;
Cos 60
0 =
&#3627409359;
&#3627409360;
Tan 60
0 = √&#3627409361;
Cot 60
0 =
√&#3627409361;
&#3627409361;

Sec 60
0 = 2
Cosc 60
0 =
&#3627409360;√&#3627409361;
&#3627409361;

Identidades Trigonométricas
Primarias.
Sen x =
&#3627409359;
&#3627408386;&#3627408424;&#3627408428;&#3627408412; &#3627408433;

Cos x =
&#3627409359;
&#3627408402;&#3627408414;&#3627408412; &#3627408433;

Tan x =
&#3627409359;
&#3627408386;&#3627408424;&#3627408429; &#3627408433;

Identidades Trigonométricas
Inversas
Cosc x =
&#3627409359;
&#3627408402;&#3627408414;&#3627408423; &#3627408433;

Sec x =
&#3627409359;
&#3627408386;&#3627408424;&#3627408428; &#3627408433;

Cot x =
&#3627409359;
&#3627408403;&#3627408410;&#3627408423; &#3627408433;

Fórmulas de las Funciones Trigonométricas
de la Suma y Diferencia de Ángulos.

Sen (A+B) = Sen A.Cos B+Cos A. Sen B
Cos (A+B) = Cos A.Cos B−Sen A.Sen B
Tang (A+B) =
&#3627408403;&#3627408410;&#3627408423;&#3627408416; &#3627408384;+&#3627408403;&#3627408410;&#3627408423;&#3627408416; &#3627408385;
&#3627409359;−&#3627408403;&#3627408410;&#3627408423;&#3627408416; &#3627408384;.&#3627408403;&#3627408410;&#3627408423;&#3627408416; &#3627408385;

Sen (A−B) = Sen A.Cos B−Cos A.Sen B
Cos (A−B) = Cos A.Cos B+Sen A.Sen B
Tan (A−B) =
&#3627408403;&#3627408410;&#3627408423;&#3627408416; &#3627408384;−&#3627408403;&#3627408410;&#3627408423;&#3627408416; &#3627408385;
&#3627409359;+&#3627408403;&#3627408410;&#3627408423;&#3627408416; &#3627408384;.&#3627408403;&#3627408410;&#3627408423;&#3627408416; &#3627408385;

Fórmulas de las Funciones
Trigonométricas del Ángulo
Duplo.

Sen 2A = 2 Sen A.Cos A
Cos 2A= &#3627408386;&#3627408424;&#3627408428;
&#3627409360;
A−&#3627408402;&#3627408414;&#3627408423;
&#3627409360;
A
Tang 2A =
&#3627409360;&#3627408403;&#3627408410;&#3627408423;&#3627408416; &#3627408384;
&#3627409359;−&#3627408403;&#3627408410;&#3627408423;&#3627408416;
&#3627409360;
&#3627408384;

Funciones
Trigonométricas del
Ángulo Mitad

Sen
??????
&#3627409360;
= ± √
&#3627409359;−&#3627408386;&#3627408424;&#3627408428;??????
&#3627409360;

Cos
??????
&#3627409360;
= ± √
&#3627408386;&#3627408424;&#3627408428; ??????+&#3627409359;
&#3627409360;

Tang
??????
&#3627409360;
= ± √
&#3627409359;−&#3627408386;&#3627408424;&#3627408428; ??????
&#3627409359;+&#3627408412;&#3627408424;&#3627408428; ??????

Para calcular la función
inversa se usa
??????
−&#3627409359;
=
&#3627409359;
??????

Funciones del Ángulo Triplo.
Sen 3w = 3 Sen w −4 Sen
3
w
Cos 3w = 4 Cos
3
w –3 Cos w
Tang 3w =
&#3627409361;&#3627408403;&#3627408410;&#3627408423;&#3627408416; &#3627408432;−&#3627408403;&#3627408410;&#3627408423;&#3627408416;
&#3627409361;
&#3627408432;
&#3627409359;−&#3627409361;&#3627408403;&#3627408410;&#3627408423;&#3627408416;
&#3627409360;
&#3627408432;

Cálculos Porcentuales. De donde:
R % de A =
&#3627408384;&#3627408433;&#3627408401;
&#3627409359;&#3627409358;&#3627409358;
A =
&#3627408401;&#3627408433;&#3627408385;
&#3627409359;&#3627409358;&#3627409358;

Proporción Porcentual

&#3627408401;
&#3627409359;&#3627409358;&#3627409358;
=
&#3627408384;
&#3627408385;
B =
&#3627408384;&#3627408433;&#3627409359;&#3627409358;&#3627409358;
&#3627408401;

R =
&#3627408384;&#3627408433;&#3627409359;&#3627409358;&#3627409358;
&#3627408385;

Interés Simple.
I = C.R.T C =
??????
&#3627408401;.&#3627408403;

T =
??????
&#3627408386;.&#3627408401;

R =
??????
&#3627408386;.&#3627408403;

Interés Compuesto.
1. Si la capitalización es
anual.
I= C [(1+R)
T
−1]

2. Si la capitalización es
n veces al año.

I = C [(1+
&#3627408401;
&#3627408423;
)
n.T
−1]

Monto a Interés Simple.
M= C (1+R.T)
Valor Actual a Interés Simple
C =
&#3627408396;
&#3627409359;+&#3627408401;.&#3627408403;

Monto a Interés Compuesto.
M= &#3627408386; (&#3627409359;+&#3627408401;)
&#3627408403;

Potencias.
??????
&#3627409358;
= 1 (∀ ??????≠0)
[(&#3627408433;)
&#3627408422;
]
&#3627408423;
= &#3627408433;
&#3627408422;.&#3627408423;

&#3627408433;
−&#3627408423;
=
&#3627409359;
&#3627408433;
&#3627408423;

(
&#3627408433;
&#3627408434;
)
&#3627408423;
=
&#3627408433;
&#3627408423;
&#3627408434;
&#3627408423;

(&#3627408410;
??????
). (&#3627408410;
&#3627408434;
) = &#3627408410;
??????+&#3627408434;

&#3627408422;
&#3627408434;
&#3627408422;
&#3627408433;
= &#3627408422;
&#3627408434;−&#3627408433;

(&#3627408410;
&#3627408434;
). (&#3627408410;
&#3627408434;
) = &#3627408410;
&#3627409360;&#3627408434;

??????
&#3627409359;
&#3627409360; = √??????
Reglas Básicas de la
división.

1.
&#3627408423;
&#3627409358;
= ∞
2.
&#3627409358;
&#3627408423;
= 0
3.
&#3627408423;
&#3627409359;
&#3627409360;
= 2n
4.
&#3627409358;
&#3627409358;
= ∞
5.
&#3627408527;
&#3627408527;
= 1
Productos Notables Fórmula del Binomio de Newton. Progresiones Aritméticas
&#3627408410;
&#3627409360;
−&#3627408411;
&#3627409360;
= (a+b) (a−b)
(a+b)
2
= (a+b) (a+b) = &#3627408410;
&#3627409360;
+2ab + &#3627408411;
&#3627409360;

(a −b)
2
= (a−b) (a−b) = &#3627408410;
&#3627409360;
−2ab + &#3627408411;
&#3627409360;

(a+b)
3
= &#3627408410;
&#3627409361;
+2&#3627408410;
&#3627409360;
b +2a &#3627408411;
&#3627409360;
+ &#3627408411;
&#3627409361;

(a −b)
3
= &#3627408410;
&#3627409361;
− 2&#3627408410;
&#3627409360;
b +2a &#3627408411;
&#3627409360;
−&#3627408411;
&#3627409361;

&#3627408410;
&#3627409361;
−&#3627408411;
&#3627409361;
= (a −&#3627408411;) (&#3627408410;
&#3627409360;
+ ab + &#3627408411;
&#3627409360;
)
&#3627408410;
&#3627409361;
+&#3627408411;
&#3627409361;
= (a +&#3627408411;) (&#3627408410;
&#3627409360;
− ab + &#3627408411;
&#3627409360;
)
&#3627408403;
?????? = (
&#3627408423;
??????−&#3627409359;
) &#3627408433;
&#3627408423;−??????+&#3627409359;
&#3627408434;
??????−&#3627409359;
??????
&#3627408527; = ??????
&#3627409359;+(n−1) d
??????
&#3627409359;= ??????
&#3627408527;−(n−1) d
d =
??????
&#3627408527;−??????
&#3627409359;
&#3627408527;−&#3627409359;

n =
&#3627408410;
&#3627408423;− &#3627408410;
&#3627409359;+&#3627408413;
&#3627408413;

??????
&#3627408527; =
&#3627408527; (??????
&#3627409359;+??????
&#3627408527;)
&#3627409360;
ó
??????
&#3627408527; =
&#3627408527; [&#3627409360;??????
&#3627409359;+(&#3627408527;−&#3627409359;)&#3627408517;]
&#3627409360;

Transformaciones Geométricas.
Traslaciones
T: (&#3627408537;,&#3627408538;) = (&#3627408537;+??????,&#3627408538;+??????)
Rotaciones.
R: (&#3627408537;,&#3627408538;)= (&#3627408537; &#3627408490;&#3627408528;&#3627408532; ??????−&#3627408538; ??????&#3627408518;&#3627408527; ??????,&#3627408537; ??????&#3627408518;&#3627408527; ??????+&#3627408538; &#3627408490;&#3627408528;&#3627408532; ??????)
Simetrías
??????
&#3627408528;: (&#3627408537;,&#3627408538;) = (−&#3627408537;,−&#3627408538;)
??????
&#3627408537;: (&#3627408537;,&#3627408538;)= (&#3627408537;,−&#3627408538;)
??????
&#3627408538;: (&#3627408537;,&#3627408538;)= (−&#3627408537;,−&#3627408538;)
Pendiente de la Recta que
pasa por dos puntos.

m =
&#3627408434;
&#3627409360;−&#3627408434;
&#3627409359;
&#3627408433;
&#3627409360;−&#3627408433;
&#3627409359;

Ecuación de la Recta que
pasa por dos puntos:

&#3627408538;−&#3627408538;
&#3627409359; = m (&#3627408433;−&#3627408433;
&#3627409359;)
Distancia de un punto a
una Recta

d =
&#3627408384;&#3627408433;&#3627409359;+&#3627408385;&#3627408434;&#3627409359;+&#3627408386;
√&#3627408384;
&#3627409360;
+&#3627408385;
&#3627409360;

Progresiones Geométricas. Ley del seno:
&#3627408410;
&#3627408402;&#3627408414;&#3627408423; &#3627408384;
=
&#3627408411;
&#3627408402;&#3627408414;&#3627408423; &#3627408385;
=
&#3627408412;
&#3627408402;&#3627408414;&#3627408423; &#3627408386;

Ley del coseno.
Cos A =
&#3627408411;
&#3627409360;
+&#3627408412;
&#3627409360;
−&#3627408410;
&#3627409360;
&#3627409360;&#3627408411;&#3627408412;

Cos B =
&#3627408410;
&#3627409360;
+&#3627408412;
&#3627409360;
−&#3627408411;
&#3627409360;
&#3627409360;&#3627408410;&#3627408412;

Cos C =
&#3627408410;
&#3627409360;
+&#3627408411;
&#3627409360;
−&#3627408412;
&#3627409360;
&#3627409360;&#3627408410;&#3627408411;

Propiedades de los logaritmos
1. &#3627408395;&#3627408424;&#3627408416;
???????????? = 1
2. &#3627408395;&#3627408424;&#3627408416;
??????&#3627409359;= 0
3. &#3627408395;&#3627408424;&#3627408416;
&#3627408410; (
&#3627408488;
&#3627408489;
)= &#3627408395;&#3627408424;&#3627408416;
&#3627408410; A − &#3627408395;&#3627408424;&#3627408416;
&#3627408410; B
4. &#3627408395;&#3627408424;&#3627408416;
&#3627408410; (AxB) = &#3627408395;&#3627408424;&#3627408416;
&#3627408410; A+&#3627408395;&#3627408424;&#3627408416;
&#3627408410; B
5. &#3627408395;&#3627408424;&#3627408416;
??????√??????
&#3627408527;
=
&#3627408395;&#3627408424;&#3627408416;
????????????
&#3627408527;

6. &#3627408395;&#3627408424;&#3627408416;
??????&#3627408526;
??????
= a &#3627408395;&#3627408424;&#3627408416;
??????&#3627408526;
7. Las cantidades negativas no tienen
logaritmos.
??????
&#3627408527; = ??????
&#3627409359;&#3627408531;
&#3627408527;−&#3627409359;

??????
&#3627409359; =
??????
&#3627408527;
√??????
&#3627408527;
&#3627408527;−&#3627409359;
r = √
??????
&#3627408527;
??????
&#3627409359;
&#3627408527;−&#3627409359;

n =
&#3627408395;&#3627408424;&#3627408416; (
&#3627408410;&#3627408423;
&#3627408410;
&#3627409359;
)
&#3627408395;&#3627408424;&#3627408416; &#3627408427;

??????
&#3627408527; =
??????
&#3627409359; (&#3627408531;
&#3627408527;
−&#3627409359;)
&#3627408531;−&#3627409359;

Suma de las medidas de los ángulos interiores de
un polígono regular.
Formula general para resolver
ecuaciones de segundo grado.
x =
−&#3627408411;±√&#3627408411;
&#3627409360;
−&#3627409362;&#3627408410;&#3627408412;
&#3627409360;&#3627408410;

∆ = √&#3627408411;
&#3627409360;
−&#3627409362;&#3627408410;&#3627408412;
Ecuación de la circunferencia con
centro en el punto (h, K) y radio R.

(&#3627408433;−&#3627408417;)
&#3627409360;
+(&#3627408434;−??????)
&#3627409360;
= &#3627408401;
&#3627409360;
ó
√(&#3627408537;−??????)
&#3627409360;
+(&#3627408538;−??????)
&#3627409360;
= R
S m ∢ i = (&#3627408527;−&#3627409360;)&#3627409359;??????&#3627409358;
&#3627409358;

m ∢ i =
&#3627409359;??????&#3627409358;
&#3627409358;
(&#3627408527;−&#3627409359;)
&#3627408527;
m ∢ e =
&#3627409361;??????&#3627409358;
&#3627409358;
&#3627408527;