Joseph Agustin Villa

ANGULOS EN GRADOS 0 15 30 45ANGULOS EN RADIALES 0 0.2617993878 0.5235987756 0.785398163SENO 0 0.2588190451 0.5 0.707106781COSENO 1 0.9659258263 0.8660254038 0.707106781TANGENTE 0 0.2679491924 0.5773502692 1ARCOTANGENTE 0 0.25605277 0.4823479071 0.66577375MAXIMA 1 0.9659258263 0.8660254038 1MINIMA 0 0.25605277 0.4823479071 0.66577375

60 75 90 105 120 1351.047197551 1.308996939 1.5707963268 1.832595715 2.094395102 2.356194490.866025404 0.965925826 1 0.965925826 0.866025404 0.707106781

0.5 0.258819045 6.12323E-017 -0.258819045 -0.5 -0.7071067811.732050808 3.732050808 1.63312E+016 -3.732050808 -1.732050808 -10.808448793 0.918430796 1.0038848219 1.071280417 1.125338833 1.1694228251.732050808 3.732050808 1.63312E+016 1.832595715 2.094395102 2.35619449

0.5 0.258819045 6.12323E-017 -3.732050808 -1.732050808 -1

150 165 1802.617993878 2.879793266 3.1415926536

0.5 0.258819045 1.224647E-016-0.866025404 -0.965925826 -1-0.577350269 -0.267949192 -1.22465E-0161.205927392 1.236576038 1.26262725572.617993878 2.879793266 3.1415926536

-0.866025404 -0.965925826 -1

SUMA DE TANGENTES

Tan (a + b)=Tan a + Tan b1 - Tan a Tan b

GRADOS MINUTOS SEGUNDOS

Angulo a 20.0336111111 20 2 1

20.7527777778 20 45 10

Tan a Tan b0.3646347135 0.3789215501

Tan a + Tan b= 0.7435562635(Tan a) (Tan B)= 0.13816795081-Tan a + Tan b= 0.8618320492

Resultado: 0.8627623726

SUMA DE COSENOS

COS(A+B)=COS A COS B= SEN A SEN B

GRADOS MINUTOS SEGUNDOS

Angulo a 45.5669444444 45 34 1

Angulo b 78.7527777778 78 45 10

sen a sen b cos a cos b0.71406891 0.9807947375 0.70007542 0.195042772

(sen a) (sen b)= 0.7003550244(cos a) (cos b)= 0.1365446512

Angulo b

RESULTADO -0.5638103732

SUMA DE SENOS

Sen(a+b)=Sen a Cos b + Cos a Sen b

GRADOS MINUTOS SEGUNDOS

Angulo a 45.5669444444 45 34 1

78.7527777778 78 45 10

Sen a Sen b Cos a Cos b0.43837115 0.4226182617 0.70669185 0.7066918533

(Sen a) ( Sen b)= 0.1852636521(Cos a) (Cos b)= 0.4994133756

Resultado: -0.3141497235

Angulo b

SUMA DE COSENO

Cos (a+b) = Cos a Cos b - Sen a Sen b

GRADOS MINUTOS SEGUNDOS

Angulo a 20.0336111111 20 2 1Angulo b 20.7527777778 20 45 10

Sen a Sen b Cos a Cos b0.3425713312 0.3543363742 0.9394918217 0.93511803

(Sen a) ( Sen b)= 0.1213854834(Cos a) (Cos b)= 0.8785357435

Resultado: 0.75715026

RETA DE COSENOS

cos a(a-b)= cos a cos b+sen a sen b

GRADOS MINUTOS SEGUNDOS

Angulo a 45.0336111111 45 2 1

Angulo b 20.7527777778 20 45 10

sen a sen b cos a cos b0.7075214657 0.3543363742 0.7066918533 0.93511803

(sen a) (sen b)= 0.2507005908(cos a) (cos b)= 0.6608402952

RESULTADO 0.911540886

RESTA DE SENOS

Cos (a+b) = Cos a Cos b - Sen a Sen b

GRADOS MINUTOS SEGUNDOS

Angulo a 45.0336111111 45 2 1Angulo b 20.7527777778 20 45 10

Sen a Sen b Cos a Cos b0.7075214657 0.3543363742 0.7066918533 0.70669185

(Sen a) ( Sen b)= 0.2507005908(Cos a) (Cos b)= 0.4994133756

Resultado: 0.2487127847

SUMA DE COSENO

RETA DE COSENOS

RESTA DE SENOS

Prestamo Plazo150000 96

Plazo Fechas de abono Importe del abono Pago con interes1 21-Apr-16 $ 1,562.50 $ 1,687.50 2 21-May-16 $ 1,562.50 $ 1,687.50 3 21-Jun-16 $ 1,562.50 $ 1,687.50 4 21-Jul-16 $ 1,562.50 $ 1,687.50 5 21-Aug-16 $ 1,562.50 $ 1,687.50 6 21-Sep-16 $ 1,562.50 $ 1,687.50 7 21-Oct-16 $ 1,562.50 $ 1,687.50 8 21-Nov-16 $ 1,562.50 $ 1,687.50 9 21-Dec-16 $ 1,562.50 $ 1,687.50

10 21-Jan-17 $ 1,562.50 $ 1,687.50 11 21-Feb-17 $ 1,562.50 $ 1,687.50 12 21-Mar-17 $ 1,562.50 $ 1,687.50 13 21-Apr-17 $ 1,562.50 $ 1,687.50 14 21-May-17 $ 1,562.50 $ 1,687.50 15 21-Jun-17 $ 1,562.50 $ 1,687.50 16 21-Jul-17 $ 1,562.50 $ 1,687.50 17 21-Aug-17 $ 1,562.50 $ 1,687.50 18 21-Sep-17 $ 1,562.50 $ 1,687.50 19 21-Oct-17 $ 1,562.50 $ 1,687.50 20 21-Nov-17 $ 1,562.50 $ 1,687.50 21 21-Dec-17 $ 1,562.50 $ 1,687.50 22 21-Jan-18 $ 1,562.50 $ 1,687.50 23 21-Feb-18 $ 1,562.50 $ 1,687.50 24 21-Mar-18 $ 1,562.50 $ 1,687.50 25 21-Apr-18 $ 1,562.50 $ 1,687.50 26 21-May-18 $ 1,562.50 $ 1,687.50 27 21-Jun-18 $ 1,562.50 $ 1,687.50 28 21-Jul-18 $ 1,562.50 $ 1,687.50 29 21-Aug-18 $ 1,562.50 $ 1,687.50 30 21-Sep-18 $ 1,562.50 $ 1,687.50 31 21-Oct-18 $ 1,562.50 $ 1,687.50 32 21-Nov-18 $ 1,562.50 $ 1,687.50 33 21-Dec-18 $ 1,562.50 $ 1,687.50 34 21-Jan-19 $ 1,562.50 $ 1,687.50 35 21-Feb-19 $ 1,562.50 $ 1,687.50 36 21-Mar-19 $ 1,562.50 $ 1,687.50 37 21-Apr-19 $ 1,562.50 $ 1,687.50 38 21-May-19 $ 1,562.50 $ 1,687.50 39 21-Jun-19 $ 1,562.50 $ 1,687.50 40 21-Jul-19 $ 1,562.50 $ 1,687.50

41 21-Aug-19 $ 1,562.50 $ 1,687.50 42 21-Sep-19 $ 1,562.50 $ 1,687.50 43 21-Oct-19 $ 1,562.50 $ 1,687.50 44 21-Nov-19 $ 1,562.50 $ 1,687.50 45 21-Dec-19 $ 1,562.50 $ 1,687.50 46 21-Jan-20 $ 1,562.50 $ 1,687.50 47 21-Feb-20 $ 1,562.50 $ 1,687.50 48 21-Mar-20 $ 1,562.50 $ 1,687.50 49 21-Apr-20 $ 1,562.50 $ 1,687.50 50 21-May-20 $ 1,562.50 $ 1,687.50 51 21-Jun-20 $ 1,562.50 $ 1,687.50 52 21-Jul-20 $ 1,562.50 $ 1,687.50 53 21-Aug-20 $ 1,562.50 $ 1,687.50 54 21-Sep-20 $ 1,562.50 $ 1,687.50 55 21-Oct-20 $ 1,562.50 $ 1,687.50 56 21-Nov-20 $ 1,562.50 $ 1,687.50 57 21-Dec-20 $ 1,562.50 $ 1,687.50 58 21-Jan-21 $ 1,562.50 $ 1,687.50 59 21-Feb-21 $ 1,562.50 $ 1,687.50 60 21-Mar-21 $ 1,562.50 $ 1,687.50 61 21-Apr-21 $ 1,562.50 $ 1,687.50 62 21-May-21 $ 1,562.50 $ 1,687.50 63 21-Jun-21 $ 1,562.50 $ 1,687.50 64 21-Jul-21 $ 1,562.50 $ 1,687.50 65 21-Aug-21 $ 1,562.50 $ 1,687.50 66 21-Sep-21 $ 1,562.50 $ 1,687.50 67 21-Oct-21 $ 1,562.50 $ 1,687.50 68 21-Nov-21 $ 1,562.50 $ 1,687.50 69 21-Dec-21 $ 1,562.50 $ 1,687.50 70 21-Jan-22 $ 1,562.50 $ 1,687.50 71 21-Feb-22 $ 1,562.50 $ 1,687.50 72 21-Mar-22 $ 1,562.50 $ 1,687.50 73 21-Apr-22 $ 1,562.50 $ 1,687.50 74 21-May-22 $ 1,562.50 $ 1,687.50 75 21-Jun-22 $ 1,562.50 $ 1,687.50 76 21-Jul-22 $ 1,562.50 $ 1,687.50 77 21-Aug-22 $ 1,562.50 $ 1,687.50 78 21-Sep-22 $ 1,562.50 $ 1,687.50 79 21-Oct-22 $ 1,562.50 $ 1,687.50 80 21-Nov-22 $ 1,562.50 $ 1,687.50 81 21-Dec-22 $ 1,562.50 $ 1,687.50 82 21-Jan-23 $ 1,562.50 $ 1,687.50 83 21-Feb-23 $ 1,562.50 $ 1,687.50 84 21-Mar-23 $ 1,562.50 $ 1,687.50 85 21-Apr-23 $ 1,562.50 $ 1,687.50

86 21-May-23 $ 1,562.50 $ 1,687.50 87 21-Jun-23 $ 1,562.50 $ 1,687.50 88 21-Jul-23 $ 1,562.50 $ 1,687.50 89 21-Aug-23 $ 1,562.50 $ 1,687.50 90 21-Sep-23 $ 1,562.50 $ 1,687.50 91 21-Oct-23 $ 1,562.50 $ 1,687.50 92 21-Nov-23 $ 1,562.50 $ 1,687.50 93 21-Dec-23 $ 1,562.50 $ 1,687.50 94 21-Jan-24 $ 1,562.50 $ 1,687.50 95 21-Feb-24 $ 1,562.50 $ 1,687.50 96 21-Mar-24 $ 1,562.50 $ 1,687.50

Intereses 0.08

Interes a pagar Saldo actual Total de abono $ 12,000.00 $ 148,437.50 $ 13,562.50 $ 11,875.00 $ 146,875.00 $ 13,437.50 $ 11,750.00 $ 145,312.50 $ 13,312.50 $ 11,625.00 $ 143,750.00 $ 13,187.50 $ 11,500.00 $ 142,187.50 $ 13,062.50 $ 11,375.00 $ 140,625.00 $ 12,937.50 $ 11,250.00 $ 139,062.50 $ 12,812.50 $ 11,125.00 $ 137,500.00 $ 12,687.50 $ 11,000.00 $ 135,937.50 $ 12,562.50 $ 10,875.00 $ 134,375.00 $ 12,437.50 $ 10,750.00 $ 132,812.50 $ 12,312.50 $ 10,625.00 $ 131,250.00 $ 12,187.50 $ 10,500.00 $ 129,687.50 $ 12,062.50 $ 10,375.00 $ 128,125.00 $ 11,937.50 $ 10,250.00 $ 126,562.50 $ 11,812.50 $ 10,125.00 $ 125,000.00 $ 11,687.50 $ 10,000.00 $ 123,437.50 $ 11,562.50 $ 9,875.00 $ 121,875.00 $ 11,437.50 $ 9,750.00 $ 120,312.50 $ 11,312.50 $ 9,625.00 $ 118,750.00 $ 11,187.50 $ 9,500.00 $ 117,187.50 $ 11,062.50 $ 9,375.00 $ 115,625.00 $ 10,937.50 $ 9,250.00 $ 114,062.50 $ 10,812.50 $ 9,125.00 $ 112,500.00 $ 10,687.50 $ 9,000.00 $ 110,937.50 $ 10,562.50 $ 8,875.00 $ 109,375.00 $ 10,437.50 $ 8,750.00 $ 107,812.50 $ 10,312.50 $ 8,625.00 $ 106,250.00 $ 10,187.50 $ 8,500.00 $ 104,687.50 $ 10,062.50 $ 8,375.00 $ 103,125.00 $ 9,937.50 $ 8,250.00 $ 101,562.50 $ 9,812.50 $ 8,125.00 $ 100,000.00 $ 9,687.50 $ 8,000.00 $ 98,437.50 $ 9,562.50 $ 7,875.00 $ 96,875.00 $ 9,437.50 $ 7,750.00 $ 95,312.50 $ 9,312.50 $ 7,625.00 $ 93,750.00 $ 9,187.50 $ 7,500.00 $ 92,187.50 $ 9,062.50 $ 7,375.00 $ 90,625.00 $ 8,937.50 $ 7,250.00 $ 89,062.50 $ 8,812.50 $ 7,125.00 $ 87,500.00 $ 8,687.50

$ 7,000.00 $ 85,937.50 $ 8,562.50 $ 6,875.00 $ 84,375.00 $ 8,437.50 $ 6,750.00 $ 82,812.50 $ 8,312.50 $ 6,625.00 $ 81,250.00 $ 8,187.50 $ 6,500.00 $ 79,687.50 $ 8,062.50 $ 6,375.00 $ 78,125.00 $ 7,937.50 $ 6,250.00 $ 76,562.50 $ 7,812.50 $ 6,125.00 $ 75,000.00 $ 7,687.50 $ 6,000.00 $ 73,437.50 $ 7,562.50 $ 5,875.00 $ 71,875.00 $ 7,437.50 $ 5,750.00 $ 70,312.50 $ 7,312.50 $ 5,625.00 $ 68,750.00 $ 7,187.50 $ 5,500.00 $ 67,187.50 $ 7,062.50 $ 5,375.00 $ 65,625.00 $ 6,937.50 $ 5,250.00 $ 64,062.50 $ 6,812.50 $ 5,125.00 $ 62,500.00 $ 6,687.50 $ 5,000.00 $ 60,937.50 $ 6,562.50 $ 4,875.00 $ 59,375.00 $ 6,437.50 $ 4,750.00 $ 57,812.50 $ 6,312.50 $ 4,625.00 $ 56,250.00 $ 6,187.50 $ 4,500.00 $ 54,687.50 $ 6,062.50 $ 4,375.00 $ 53,125.00 $ 5,937.50 $ 4,250.00 $ 51,562.50 $ 5,812.50 $ 4,125.00 $ 50,000.00 $ 5,687.50 $ 4,000.00 $ 48,437.50 $ 5,562.50 $ 3,875.00 $ 46,875.00 $ 5,437.50 $ 3,750.00 $ 45,312.50 $ 5,312.50 $ 3,625.00 $ 43,750.00 $ 5,187.50 $ 3,500.00 $ 42,187.50 $ 5,062.50 $ 3,375.00 $ 40,625.00 $ 4,937.50 $ 3,250.00 $ 39,062.50 $ 4,812.50 $ 3,125.00 $ 37,500.00 $ 4,687.50 $ 3,000.00 $ 35,937.50 $ 4,562.50 $ 2,875.00 $ 34,375.00 $ 4,437.50 $ 2,750.00 $ 32,812.50 $ 4,312.50 $ 2,625.00 $ 31,250.00 $ 4,187.50 $ 2,500.00 $ 29,687.50 $ 4,062.50 $ 2,375.00 $ 28,125.00 $ 3,937.50 $ 2,250.00 $ 26,562.50 $ 3,812.50 $ 2,125.00 $ 25,000.00 $ 3,687.50 $ 2,000.00 $ 23,437.50 $ 3,562.50 $ 1,875.00 $ 21,875.00 $ 3,437.50 $ 1,750.00 $ 20,312.50 $ 3,312.50 $ 1,625.00 $ 18,750.00 $ 3,187.50 $ 1,500.00 $ 17,187.50 $ 3,062.50

$ 1,375.00 $ 15,625.00 $ 2,937.50 $ 1,250.00 $ 14,062.50 $ 2,812.50 $ 1,125.00 $ 12,500.00 $ 2,687.50 $ 1,000.00 $ 10,937.50 $ 2,562.50 $ 875.00 $ 9,375.00 $ 2,437.50 $ 750.00 $ 7,812.50 $ 2,312.50 $ 625.00 $ 6,250.00 $ 2,187.50 $ 500.00 $ 4,687.50 $ 2,062.50 $ 375.00 $ 3,125.00 $ 1,937.50 $ 250.00 $ 1,562.50 $ 1,812.50 $ 125.00 $ - $ 1,687.50

1 1.0079

HHidrógeno

1 1.0079

HHidrógeno

3 6.941

LiLitio

3 6.941

LiLitio

11 22.990

NaSodio

11 22.990

NaSodio

19 39.098

KPotasio

19 39.098

KPotasio

37 85.468

RbRubidio

37 85.468

RbRubidio

55 132.91

CsCesio

55 132.91

CsCesio

87 (223)

FrFrancio

87 (223)

FrFrancio

NUMERO NOMBRE SIMBOLO MASA ATOMICA

1

2

3 Litio

4

5

6

7

8

9

10

11 Sodio

12

13

14

15

16

17 Potasio

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37 Rubidio

38

39

Hidrogeno

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55 Cesio

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87 Francio

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117118

EDO. DE AGREGACION VALENCIA

X Y Y=1/X-1.5 -0.67 -1.5 -0.67-1.2 -0.83 -1.2 -0.83-0.9 -1.11 -0.9 -1.11-0.6 -1.67 -0.6 -1.67-0.3 -3.33 -0.3 -3.33

0 0.00 0 0.000.3 3.33 0.3 3.330.6 1.67 0.6 1.670.9 1.11 0.9 1.111.2 0.83 1.2 0.831.5 0.67 1.5 0.67

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

Column B

Column C

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

-4.00

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

Column B

Column C