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Monday, November 29, 2010

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deradicales.blogspot.com Basic Concepts of Trigonometric ratios


trigonometric ratios are usually defined as the ratio between two sides of a triangle associated with the angles. The trigonometric functions are functions whose values \u200b\u200bare extensions of the concept trigonometric ratio right triangle drawn on a unit circle (radio unit). Modern definitions describe them as infinite series or as the solution of certain differential equations, allowing their extension to positive and negative values, and even complex numbers.

There are six basic trigonometric functions. The last four, are defined in relation to the first two functions, but can be defined geometrically or through their relationships. Some features were common in ancient times, and appear in the first tables, but not currently used, for example, versene (1 - cos θ) and exsecante (sec θ - 1).

Sunday, November 28, 2010

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Things about "Pi"

1. Is the ratio of the length of the circumference and diameter of the corresponding circle.
2. It is the sixteenth letter of the Greek alphabet .
3. Is an irrational number transcendent.
4. The fractional number closest to it is 3 1 / 7.
5. Also called ludolfino number in honor of Ludolf Van Ceulaer (1540-1610), who could determine its value up to 35 decimal places.
6. According to Archimedes its value should be between: 3 1 / 7 and 3 10/71. (3 1 / 7 = 3.14084, 3 10/71 = 3.14285).
7. William Shanks , investing more 20, calculated the 707 decimal places, but later research found that the amount allowed had error 528.
8. In the binary numbering system = 11.001001000011111101101010.
9. = 3.14159265358979323846264338327950288 ...
10. In 1949 the ENIAC computer were estimated at just over 70 hours of their first 2000 decimal places.
11. In 1954, numbers reached 3093 in 13 minutes.
12. In 1959 figures were calculated 10000 1 hour and 40 minutes decimal.
13. And the July 29, 1961 IBM reached a decimal expansion to the figure of 100,265.
14. Finally it is said that there was a chick so smart that instead ple say 3.14159 :) said.

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Trigonometry and trigonometric ratios.


The Trigonometry is a branch of mathematics, whose etymological meaning is "the measurement of triangles " .

Trigonometry is the branch of mathematics s that studies the relationships between angles and sides of triangles. For this it uses the trigonometric ratios, which are frequently used in engineering calculations.

In Overall, the trigonometry is the study of functions within , cosine ; tangent , cotangent, secant and cosecant. Directly or indirectly involved in the other branches of mathematics and applies in all areas where measures are required accuracy. Trigonometry applies to other branches of geometry , as is the case study areas in geometry of space .

has many applications: triangulation techniques, for example, are used in astronomy to measure distances to stars next, in measuring distances between points geographic and navigation systems by satellite .


Trigonometric ratios

The triangle ABC is a triangle in C, we will use to define the reasons sine, cosine and tangent of the angle  \alpha \, , corresponding to the vertex A , located in the center of the circle.

  • The within (abbreviated as sen or without to be called "breasts" in Latin) is the ratio of leg on the opposite hypotenuse,
    \operatorname {sen} \, \alpha =    \frac{\overline{CB}}{\overline{AB}} =    \frac{a}{c}
  • The cosine (abbreviated cos ) is the ratio of the hypotenuse adjacent side,
    \cos\alpha =    \frac{\overline{AC}}{\overline{AB}} =    \frac{b}{c}
  • The tangent (abbreviated as or tg) is the ratio between the leg opposite the side adjacent,
    \tan\alpha =    \frac{\overline{CB}}{\overline{AC}} =    \frac{a}{b}

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The history of calculators,




A calculator started: The A tobacco

The first calculators were abacus, often constructed as a wooden frame with beads sliding on wires. The abacus was used for centuries before the adoption of the writing system of Arabic numerals, and even remain em ployees by merchants and clerks in China and other parts of the world do .

XVII Century

William Oughtred invented slide rule in 1622, being revealed by student Richard Delamain in 1630. Wilhelm Schickard built the first automatic calculator call ada "Calculator Clock" in 1623.

nineteenth century

Charles Babbage developed the concept further , opening the way to programmable computers, while the machine who built was too heavy to be operable.

The last quarter of the nineteenth century witnessed significant progress in mechanical calculators:

  • Frank Baldwin in 1872 in the United States invented the calculator Gear, which was also independently developed two years later by WT enSuecia Odhner. Odhner model and similar to other companies sold several thousand units in 1870.
  • E. Dorr Feltinventó in the United States comptómetro in 1884, the first machine operated for keys that allow adding and calculating (as opposed to previous designs that required to operate separate levers). In 1886 he joined with Robert Tarrant to establish it Felt & Tarrant Manufacturing Company, which produced thousands of comptómetros.
  • In 1891 William S. Burroughs began to market his summing calculator printer. The Burroughs Corporation became one of the leading companies in the market for accounting machines and computers.
  • Calculator Millionaire was made in 1893. It allowed direct multiplication by any digit.

In mid-1980 to currently

In March 2002 HP announced that it stopped making calculators, which was difficult to ccept by some fans of the company's products, taking particular range HP-48 base extremely loyal customers .

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Archimedes and some things about the volume of the sphere





Many know the learned Archimedes, especially for the levers. Volume calculation the area was one of the more believed that Archimedes discoveries of all he did in his life. He came to demonstrate in a very original way that the volume of the sphere is equal to two thirds of the volume of circular cylinder confined to it. He was so impressed that he himself (perhaps because at that time there was talk of perfect bodies) who commanded in his grave this figure is recorded in memory of the best of their ideas.

Archimedes figured a hemisphere and next to it a right circular cylinder and right cone, both as a base circle of the hemisphere.

obtained in the cylinder is a circle of radius R (note that the radius is half the diameter d). In the area also will be a circle, but his radio depends on the distance d. Looking at the figure below, remembering the Pythagorean theorem, you can easily write that if the radius of the section is r, then d2 = r2 + R2.

cylinder = Volume Volume Volume + cone hemisphere
But, like Archimedes well knew,
Volume cylinder = PR3;
Cone Volume = PR3 / 3 and so was
hemisphere volume = 2PR3 / 3 Volume sphere = 4PR3 / 3.

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Pythagoras Pythagoras (580-500 JC) was a Greek philosopher and mathematician. He was born on the island of Samos and settled in southern Italy, where he founded a religious school, politics and philosophy. The Pythagoreans Studies on odd and even numbers, prime numbers and square. In geometry, his great discovery was the theorem that bears his name, which states that "the square of the hypotenuse" of a right triangle is equal to "the sum of the squares of the other two sides, the legs.

Theorem of Pythagoras states that in a triangle the square of the length of the hypotenuse (the longest side of triangle) is equal to the sum of the squares of the lengths of the two legs ( the two shorter sides of the triangle, which form the right angle). If a right triangle has legs of lengths and, and the measure of the hypotenuse is, states that:
C2 = A2 + B2
The Pythagorean Theorem is so named because their discovery rests on the Pythagorean school. Earlier in Mesopotamia and Ancient Egypt was known triples of values \u200b\u200bthat correspond to the sides of a triangle, and used to solve problems pertaining to the said triangles, as shown in some tablets and papyrus , but has not endured any document theoretically expose their relationship. The pyramid of Khafre , dating from the century XXVI a. C. , was the first great pyramid was built based on the so-called sacred Egyptian triangle ,

Wednesday, November 24, 2010

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Pythagorean theorem Areas of Klerksdorp. Areas "aliens?


This post is deals a sphere found adas in Africa that

dating has 2,800 cc million to dren, strange is your form as q ue all have n a pattern so so fistic b ien fact has ce impossible been that alla created by the nature and many least cho human , one of the many secrets innentendibles of our planet .

The Klerksdorp areas are little balls of pyrite that have been found in Ottosdal ( South Africa ) on strata prechamber factories of 2,800 million years ago by my genres. These are out in K Museum lerkdorp. is said that its spherical shape and fine grooves Sól or may have left intelligent beings . This view is reflected in the work prohibited Archaeology of Michael Cremo. However,

pyrite nodules are probably of metamorphic origin, and nodules of "goethite" Wear formed pyrite. In an article on this subject Paul Henrich emphasizes that l as sources of C rowing, in regards to areas s upuestamente 'abnormal' , were in fact W eekly World

News (News World Week), a source hardly c abe accept as serious and re bitch.

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truncated cone or truncated cone



The truncated cone, cone Garofalo truncated or trunk is a volume of revolution generated by a trapezoid rectangle as taking the side spin axis perpendicular to the bases.

A truncated cone straight, parallel database, cone portion is between two planes that intersect and are perpendicular to its axis. Is determined by the radii of the bases, R r, the height, h, and generating, g, which gives the following rel ation:



The lateral area of \u200b\u200ba truncated cone can be found by solving the following equation:



The area of \u200b\u200ba truncated cone (area more lateral area of \u200b\u200bthe upper and lower circles) can be found using the formula:



The volume of a truncated cone can be found using the following formula:

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Australian Aboriginal children can count without numbers
Carlos Martin October 13, 2008
According to a new study of Australian Aboriginal children by the University College London and The University of Melbourne, knowing the words for numbers is not necessary to tell.
The study examined certain indigenous Australians who have very limited vocabulary for numbers, working with children aged four to seven years, two indigenous communities difierente language. In both languages, there are words for one, two, few and many. And there seems to be no move to the numbers.
In the study, we found that this lack of words or gestures for numbers in the children examined did not prevent a series of tasks related to them.
The results of this new study suggest, therefore, that human beings possess an innate mechanism for counting, which may develop differently in children condiscalculia, and that the lack of a vocabulary for numbers should not blind us to perform numerical tasks that do not require words for numbers. This innate system for counting allows us to recognize and represent the number of objects in a set.

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Monday, November 22, 2010

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Polyhedra in everyday life. SOCCER BALL






















Soccer balls have always been made with 12 pentagons and 20 hexagons (truncated icosahedron), though some have changed today other polyhedral shape rounder ( the small rhombicosidodecahedron) that has 20 triangles, 30 squares and 12 pentagons


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Friday, November 19, 2010

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Wednesday, November 17, 2010

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Problems deals, token, proportions and percentages.

1 - Ana buy 5 kg of potatoes, if 2 kg cost € 0.80, how much pay Ana?

2 - 3 workers built a wall in 12 hours, how long will it take 6 workers to build it?

3 - 11 workers tilling a rectangular field 220 m long and 48 wide in 6 days. How many workers will be needed to carve another similar field of 300 m long and 56 m wide in five days?

4 - Six taps, take 10 hours to fill a tank of 400 m³ of capacity. How many hours does it take four taps to fill 2 tanks of 500 m³ each?

5 - The price of a computer is 1200 € excluding VAT. How much to pay for it if the VAT is 16%?

6 - When buying a monitor that costs 450 € do us a discount of 8%. How much do we pay?

7 - three individuals were associated with providing 5000, 7500 and 9000 €. After a year they have won € 6 450. How much for each one if they make a deal directly proportional to the capital contributed?

8 - All get a lot of money, three people, directly proportional to 3, 5 and 7. Knowing that the second is that € 735. Find what belongs to the first and third.

9 - Deal € 420, including three children in parts inversely proportional to their ages, who are 3, 5 and 6.

10 - What decimal number corresponding to each of these percentages? 33% 7% 5.4% 145% .

11 - Calculate 7% of 5 420.

12 - Calculate the percentage that represents 78 of 125.


If you need answers to the proposals, ask your teacher or written comments to place the responses on this issue or other issue that has been published. Luck !!!!!!!!!!

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We present a series of situations to solve problems using real numbers.

1 - Calculate what fraction of the unit represents: a) Half of the half. half b) Half of the third party. c) The third part of the half. d) Half of the quarter.

2 - Two cars A and B make the same journey of 572 km. L cam car A travels the 5 / 11 of the way when B has crossed the 8 / 13 of it. Which of the two goes first? How many miles he travels each cam?

3 - few years ago Peter was 24, representing as the 2 / 3 of its current age. How old is Peter?

4 - In local elections in a village, 3 / 11 of votes were cast for the party A, 5 / 10 for the match B, 5 / 14 to C and the rest for the match D. The total score has gone from 15,400 s. Calculate: 1 - The number of votes obtained by each party. 2-The number of abstentions aware that the number of voters is 5 / 8 of the electorate.

5 - A father distributed between their children € 1800. The larger one gives 4 / 9 of that amount, the medium 1 / 3 less than the rest yal. How much was each? What fraction of the money was the third?

6 - Write in decimal form 3 / 7 and 9 / 11.

justify previously, if the decimal will be accurate or newspaper.

7 - Write in scientific notation following numbers : a) 125 100 000 000. b) One-tenth of one ten thousandth.

8 - Express in scientific notation: a) The speed of light is three hundred million meters per second. b) The influenza virus has a diameter in mm of five hundred thousandths. c) In the Milky Way is about one hundred and twenty billion stars.

Tuesday, November 16, 2010

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bisector of a segment

bisector.

is an important locus for working in different situations in the classroom or in real life situations. For example, three neighbors who want to share the same warehouse to save a seeder, but nobody wants to make a further journey to get there.
We ask ourselves, how to resolve the situation? If setting forth the names with the letters A, B and C, knowing that are not aligned, we can perform the following picture:

A
B


C

Noting the properties that meet the points of the bisector and then his path, I hope you can give a solution to this situation.

We know that distance between facilities is, between A and B is 50 km, between A and C is 45 km and between B and C is 62 km.

Remember that everyone wants to be at the same distance from the house. You can ask your teacher to give you any other information, although I would not be necessary if you can focus on both videos. LUCK with the slogan.