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Harris Dr. Carlos Emilio Carlos Emilio Hernandez
Mr. Harris Ferrer

ABSTRACT The main objective of this study is to determine the correlation between aerobic capacity and physical work in athletes involved in athletics.
In Sports Medicine, indicators of aerobic capacity and physical work influence the way sports, both are determined through laboratory equipment and instruments that allow us to know these variables by the direct method.
The field clinic provides information in an indirect way, allowing the significant changes seen in the athlete, to increase these indicators through consistent and systematic training.
was performed a treadmill test and a laboratory at veloergómetro to 9 athletes of both sexes (5 males and 4 females), including within high performance, events and middle distance background and the results compared with of themselves ern to a test field, which is to run 12 minutes without any external stimulus to mediate.
The results were: the values \u200b\u200b(both sexes) of PWC170/Kg VO2/Kg product and workloads on the treadmill and veloergómetro, are positively correlated (r = 0.71 and 0, 80) with the results of these variables to make the Cooper test to determine aerobic capacity and integrated into Formula Karpman calculations for determining physical work capacity.
Integrating Test-Karpman Cooper has a high degree of application and use in obtaining operational parameters.
Keyword: Athletics, maximum oxygen consumption and physical work capacity relative to body weight (V02/Kg y PWC170/Kg)
SUMMARY
The main objective of this study is to know the correlation of de aerobic capacities and the physical work in athletes who practice athleties.
In the Sport Medicine, the indicator of aerobic and physical work capacities have certain influence in the sport way both have being determine by mens of equipments and laboratory instruments. The give us the opportunity to know this variables by means of a direct method.
The ground clinic give us and indirect way of information. It permits us to appreciate significants changes in the athlete with the indicators growing or by means of a sistematic training.
The test were made in the lab on a treadmill and on a cycle-ergometer to nine athletes of both sexes, five males and four females within the high perfomance in the long distance and half long distance events, and the results were compared with those of themselves when they realized the test on the ground that consisted on running during 12 minutes without any external stimulus.
The results that have been found are: the values of the VO2 /Kg and those of the PWC170/Kg (in both sexes), as a result of the workload on the treadmill and a cycle-ergometer wich are positively correlated (r = 0,71 and 0,80) with the results obtained on these variables when they realized the Cooper´s Test to determine the aerobic capacity and to integrate the Karpman´s formula in the calculations in order to determine the physical work capacity.
The integration of Cooper-Karpman Tests has a high grade of utilization and application in the obtainment of the functional parameter.
Key Word: Athleties, Maximal Oxygen Output, Physical Work Capacity related to the body weight (VO 2 / kg and PWC170/Kg)

Introduction to 9 were studied athletic training athletes and the results obtained in the laboratory and the field is were compared with themselves.
The main objective of this study is to compare both tests to determine their correlation, and the degree of significance in athletes involved in athletics.
The findings of VO2 max and PWC170 and their values \u200b\u200brelative to body weight (VO2/Kg and PWC170/Kg) in applying the test batteries in different conditions (laboratory and field) in both sexes, the correlation (r = 0.71 and 0.80) and no significant differences between these variables. We provide the information directly and indirectly, that allows us to appreciate the possibilities that the athlete has to absorb the constant workload on its way to the way sports. MATERIAL AND METHOD

9 athletes were studied, belonging to the National Athletics Centre in Santiago de Cuba, at the beginning of his general training. Of these, five males, three of them middle-distance train and two background; and four female middle-distance train. The athletes were subjected to physical load on a treadmill with gas analyzer Erich Jaeger firm, which had the following features: applied loads of 2 minutes each, with varied slope on the mat, with speeds increasing from 8 to 24 km / h.
Every 30 seconds were recorded VO2 max values \u200b\u200bof heart rate (fc) and VO2/Kg
The scheme was applied loads up to the exhaustion of the athlete. Distance was calculated, taking into account the speed of each of the applied loads. Later
athletes underwent exercise testing in the mechanical meter mark veloergó Monark, where sub-maximal loads applied. The powers of the charges were calculated using the nomogram used in our center (1) to determine the PWC170 (Tables I and II).
This determination is based on applying two workloads (N1 and N2) with a duration of 5 minutes each and with a rest period between two to three minutes.
Karpman and colleagues. (2) recommend choosing the powers (N1 and N2) so that fc.1 achieve 100 to 120 and fc.2 of 140 to 170 contractions per minute. For use stethoscope heart rate, measuring the same at rest and within 15 seconds of each of the charges; through fc. 1 obtained, we calculate N2 where: PWC170 = N1 + (N2-N1) 170 -f1/f2-f2 and knowing the athlete's body weight to calculate the PWC170/Kg each.
In medical management training, are important laboratory tests in the same magnitude must be assessed in the field clinic.
In order to correlate these laboratory tests on the ground, after a week that were recovered from the laboratory tests, apply to the 9 athletes in question, the Cooper test, which consisted of a race for 12 minutes, without any external stimulus to mediate with a view to obtaining a specific brand for that time and complete it, using the stethoscope take fc in a time of 10 seconds, multiplying by 6, thus knowing the same to the minute calculated the distance traveled. Using
Cooper's formula for the VO2/Kg Max (Max VO2/Kg = Speed \u200b\u200b[Mts x min] x 0.2 + 3.5) (3) got the Max VO2/Kg indirect, then multiplying this by the body weight we find the VO2 Max athlete
PWC170 to get the starting point was the formula Karpman and clearing the same for the calculation of elite athletes, we have: VO2 max = PWC170 x 2.2 + 1070; clearing the same then: PWC170 = Max VO2 - 1070 / 2,2 substituting the value of VO2 max, obtained by each athlete in the formula set forth above was determined PWC170 and the PWC170/Kg. The statistical analysis was conducted by the Department of Computing IMD (Institute of Sports Medicine), using a mini computer that was determined LTEL/20 central tendency parameter arithmetic mean (x) and dispersion: the standard deviation (SD).
was determined using the Student test for paired samples, if there are significant differences between the studied parameters.
statistical analysis was performed to find the Pearson correlation coefficient. RESULTS

The values \u200b\u200bof VO2 max and PWC170, and their respective values \u200b\u200brelative to body weight in men, in applying the battery of tests in different conditions (laboratory and field) are shown in Table III. Linear correlation between indicators VO2 Max, Max VO2/Kg, PWC170, and Max PWC170/Kg VO2/fc, but not with the fc, distance traveled and time spent in the race. As
significant differences between the values \u200b\u200bobtained in the fc distance traveled and time spent in the race (p 0.05) in oxygen pulse indicators, fc., Distance traveled and time spent (Table IV) DISCUSSION

In Table III, whose values \u200b\u200bcorrespond to the athletes, the VO2 max, VO2 max / kg, PWC170, PWC170 / kg and VO2 max / fc product of workloads in the conveyor belt, are positively correlated (r = 0, 91 to 0.71 - 0.91 - 0.80 and 0.90) with the results obtained in these variables to make the Cooper test (3) to determine aerobic capacity and integrated into the formula calculations Karpman (2) for determining the physical work capacity . No significant differences in the indicators mentioned above and if the heart rate, distance traveled and time spent in the race (p 0.05).
is very likely that the arithmetic mean of fc (185 ppm) reported in the "clinic on the ground" made on the court, exceeds that found in the laboratory (160 ppm), for work in less time -12 minutes - these athletes traveled 294 meters more than that calculated on the mat stock in the laboratory, which infers a greater effort, we should also add the speed of the headwind and the irregularity of the track (curves), which logically act negatively in the performance of the activity. Hi
VO2/Kg These values \u200b\u200bare very consistent with those reported (4, 5, 6), for athletes whose quality is fundamental to develop overall strength.
Table IV shows the results obtained by female athletes, appreciating linear correlation variables VO2 max, VO2 max / kg, PWC170, PWC170/Kg (r = 0.91 - 0.71 to 0.91 - 0, 80) respectively, in the statistical analysis of laboratory tests and clinical in the field.
in this group is significant difference (p 0.05) VO2 max indicators / fc, fc, trip distance and time spent.
In the field test the arithmetic mean of the fc was 180 ppm. We can infer that this is because the athletes on the field at one time ran 260 meters lower than those in laboratory. Adding accidents listed when making the analysis in males.
These results are consistent with those reported by (4.6). At the clinic on the ground, the two groups, male and female athletes were used to fund the race done, this is shown by the distance traveled since the field was higher than in performed in the laboratory and in less time, plus increased heart rate (Tables III and IV). We note that two of these athletes was the second time in his career played on the treadmill and the rest first.
Our results confirm once again that even without sophisticated means, we can obtain data that are closer to the reality of the state of assimilation of workloads by athletes, just have the clinic on the ground with batteries that will truly foster desired goal; taking in our favor being implemented on the means of training and competition. At no point denying development acquiring science and technology with the application of highly developed equipment to dig into the changes that originate in the human body to cope with stress tests, for which we are unprepared, without a previous exercise routine.

Table I - Determination of the first load lock-jo (N1) in the Test PWC170 for the athlete's pulse acos-graph and body weight. CONCLUSIONS


1 .- Integrating Test-Karpman Cooper has high degree of application and use in obtaining operational parameters. 2 .- There
linear correlation between fundamental variables studied.
Table III - Arithmetic mean and standard deviation standard variables obtained in the laboratory and clinical research in the field. Male Group
Table IV - Arithmetic mean and standard deviation of the variables obtained in the laboratory and clinical research in the field. Female Group

Bibliography 1 .- STOIDA, Y., M. GONZALEZ "On the dosage loads veloergómetro PWC170 Test." Supplement # 4 INDER Scientific Technical Bulletin. Cuba. P. 59-68. 1979
2 .- Karpman, VL et al. , "Izledovanic fizicheskov robotosposobnosti or sportsmenov", Moscow. Evs.1974
3 .- J. PADILLA "Effect of sporting competition on blood plasma glucose concentration." Medicine Edition and Science. P. 1910-1916 Year I No. 6, July 1985. 4 .- HERNANDEZ
HARRIS, CE, Nicot G.: "Comparison and correlation between lipids, lipoproteins, indicators of aerobic capacity and anthropometric variables of athletes and nonathletes" Working to qualify for the title of Specialist 1st. Degree in Sports Medicine, Institute of Sports Medicine. 1983
5 .- AMARO, S., Nicot, G.: "Hormonal response to maximal physical load in endurance athletes." Edition. Sports Medicine and Sports. Vol 2 No. 1, 1991
6 .- DRAGAN, I. "General Physical Capacity." The Olympic Book of Sports Medicine. Volume I. Page 89-98. 1988.

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Peculiarities of Physical Training in Athletics. Capacity building. Media and fundamental methods

physical training is one of the most important components for Athletic Training, due to the high level of implication that has the same optimal in achieving competitive returns.
physical preparation, has three classifications (Platonov, 1995), general, special or specific auxiliary, which apart from its objectives and tasks, as a whole is geared to the needs and / or requirements of the sport practice .
In the case of athletics, a sport highly complex, given the wide range of evidence presented by the official competition program, it is necessary to particularize the work towards the development of physical training, for each of the areas in charge of gathering the relevant disciplines within the same classification, as are the area of \u200b\u200bspeed (flat, hurdles), area of \u200b\u200bmiddle distance and background, area of \u200b\u200bthrows, jumps and area events or multiple testing. Particularized
work areas was mainly the fact that although there are similarities between the tests within the same classification, the technique of their execution is completely different and therefore also the types of efforts to do so the preparation physics must directly contribute to the development of energy systems that guarantee the expense caused by each effort to performance. Introduction

physical training is one of the most important components for Athletic Training, due to the high degree of involvement that has the same optimal in achieving competitive returns
Definition of Physical Fitness (Platonov, 1995): The application a set of physical exercises (usually outside those used in the sport), rationally designed to develop and improve the qualities of perception - the person drive for greater physical performance.
not a simple imitation of the exercises exemplified by the coach, nor implementation of a plan drawn empirically. It is a complex problem that demands the most rational view supported by the principles adopted by the research in the field of physical activities - sports. A knowing and voluntary exercise with clearly defined objectives.
As part of the Athletic Training, physical training should meet the needs of the sport is practiced. Development

Physical preparation is classified as general, special or specific auxiliary (Platonov, 1995).
General Physical Preparedness (GPP):
means the harmonious development of physical capacity - driving without reference to a particular sport, its development has great influence on physical performance.
Physical Fitness Assistant (PFA):
is based on a prior general fitness aims, perform the basic preparation necessary for the assimilation of large volumes of work, focused on developing specific skills or special.
should increase the working capacity of the person so that it can withstand heavy workloads, and to obtain optimal recovery after the conduct.
Specific Physical Preparation (ETP):
is carried out in strict compliance with the requirements of the sport in which the athlete must compete. As the physical capabilities - are driving more, and its manifestations, improving each claim a distinct work.
Each of these classifications has its own particularities in terms of objectives, skills to develop means and methods are concerned, in line with the characteristics of each sport or form.
Athletics is one of the most complex sport in terms of planning about the fitness of its practitioners because of the wide range of disciplines that make up its competitive program official if it is true that entre las pertenecientes a una misma área existen notables similitudes, sobre todo en cuanto a la utilización de algunos medios y métodos dentro del proceso de preparación, también es preciso señalar que entre éstas, de igual modo, se ponen de manifiesto marcadas diferencias, con énfasis en la ejecución técnica de las mismas y por ende con el tipo de esfuerzo a realizar por parte del atleta; esto último relacionado directamente con el desarrollo de los sistemas energéticos, encargados de garantizar la consecución de un óptimo rendimiento.
Dada la cantidad y variedad de disciplinas competitivas que posee el Campo y Pista, las mismas se agrupan en un total de cinco (5), grandes áreas que are as follows. Speed \u200b\u200b
Area. Middle Area Fund and the Fund. Jumping Area. Launch Area. Area Events and Multiple Tests. Taking into account the above features inherent to athletics, as well as the methodological preparation for the physics, as biopedagógico and psychological basis of the process of Athletic Training, we will illustrate through examples, how to carry out development fitness in each of their classifications.
For this we take as a reference to the speed area, specifically the section where the so-called races fall flat. Disciplines

100 m 200 m 400 m 4 x 100 m 4 x 400 m
Conclusions
physical preparation, through its various classifications (general, special and auxiliary) has a high degree of influence on the performance of athletes. Given the nature of athletics, each of these classifications must be tailored to the needs or specific requirements of the test or training modality.

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WEIGHT TRAINING FOR ENDURANCE ATHLETES

The program of resistance training should, in essence, have a similar pattern here described. One of the most common mistakes among endurance athletes is that strength training does not change. Athletes continue to perform work on circuit or large amounts of series with many repetitions per set during the years of working well with very low intensities. Tables 1 and 2 show how should be designed training programs for endurance athletes.

Note that all jobs are very different from each other. As mentioned above, many athletes choose to train in the same way throughout the year, but this method takes advantage of the body's ability to adapt specifically to the training variables that present during each phase of training. The endurance athlete should not aim to achieve their best times during the off-season because at that time no race to compete. Similarly, athletes should not perform resistance training of high intensity during this period. When athletes are in full season of competition, need to stay healthy and fast. The most intense work but with less volume are designed to meet these objectives. Table 3 explains the reasoning behind the key differences between the two types of training.
Most endurance athletes have little experience in strength training, do not appreciate the benefits that intense training can give you strength for your sport. Some athletes fear that strength training unnecessarily increase their body size or high intensity training will cause a decrease in maximum oxygen consumption it would make them slower. These fears are not unfounded, as weightlifting causes an increase in muscle tissue and high-intensity work with long pauses have the effect of reducing the aerobic efficiency. However, these adjustments will occur if such practice are maintained for long periods (several months). But when this type of training is attached to the work in the short term (two different periods of four weeks), the adaptations that occur are mainly neural level, which means that it produces only a small physiological change that can adversely affect performance endurance athletes (1).
Even those who engage in aggressive program of resistance training can do so for the wrong reasons. They believe that the only time in which to be fast and powerful real benefit to endurance runner's during the final sprint or during the ascent of a slope difficult.
Suppose, for example, that could reduce the number of strides that performs during a race by 10%. Do you think this will allow you to be faster during a race? Runners tall with long strides longilíneos are often the envy of the lower corridors. You can not change your height, but can improve your career stride mechanics of learning a better stride, and also increasing the amount of force applied to the floor on every flight. A small increase in strength will allow you to have a slightly longer stride.
For example, assume that a hypothetical corridor is stride length of five feet. During a 5km race held about 3280 strides. An increase in stride length of only 6 inches will allow the individual making strides 2981, a reduction of 9%. The training of high intensity strength, and especially some forms of plyometric training, is the best way to increase stride length, and thus running economy.

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THE TRACK WITH WOMEN'S PERFUME

"The kids did not give ball, my boyfriend was the only sport, and even went dancing." That phrase would sound strange in any modern woman, globalized, invaded by beauty magazines and coquetry. Noemí Simonetto But in 1940, was a lifestyle apasionante.Cuando appointing Naomi Simonetto, referring to an eminence of the national sport female. The athlete Buenos Aires in particular a trio with the Argentine Olympic swimmer and tennis player Jeannette Campbell Gabriela Sabatini: they are the only women who got silver medal in individual specialties Olímpicos.Finalizada Games World War II, the delegation of Argentina with 350 representatives, of which only 11 were women, departed from the port of Buenos Aires on a ship called "Brazil" for London, to play high level sports event mundial.Simonetto, aged 22, was criticized by I suggested that journalists should be devoted to a single discipline and, thus, try to improve their brands. But Naomi liked "All disciplines", and almost all had record sudamericano.En London 1948, Simonetto was noted in four tests, but the fixed idea was to win the 80 meters hurdles. Finally reach the semifinals, where a controversial decision would be third, behind the French Mongirou who crossed her and hit her lifeline to be second. For Naomi was the long jump as a possibility for Wembley Stadium medalla.El prepared to meet the women's long jump for the first time in the Olympics, as stipulated a minimum mark to be overcome to advance to the final: 5, 3 meters. That mark was surpassed only by Simonetto and two athletes, so the organizers classified "advantage" to five competitors más.De these five competitors would the gold medal. Olga Gyarmati of Hungary, who with a jump of 5.695 meters to relegate to second place athlete in Argentina, which jumped 5.605 meters. "There was a jump that I wanted to post. I never knew why, but I did not speak because he spoke no English, "said Simonetta. Finally won the silver medal, but it was the Argentine people who honored with recognition. And the recognition weighs ounces of gold. Statements taken from
* Mystic Magazine. Posted

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Other tips to prevent problems when doing strength training with weights are:

■ Adapt the computer the size of the adolescent. ■ ensure that adolescents have the correct posture. ■ good knowledge of exercise technique and stop exercising if you notice your teen is using an incorrect technique. ■ There must be an instructor for every two or three children. If you are young then there may be 10 per instructor. ■ Each adolescent and child should have a journal to make notes of your training program ■ Each exercise session should last about 60 minutes. It is important to start with a warm-up period (10 minutes) and end with a period of stretching (10 minutes). ■ Recommended for arm exercises insert leg exercises, they should be slowly and through the whole arc of movement to a specified intensity in each individual case

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Weights and adolescents: Recommendations for training

To avoid injury during strength training with weights is recommended: A medical evaluation before beginning the program. Supervision by experienced professionals. Use light weights to allow at least seven repetitions. Should not be allowed to lift weights, raised in power or bodybuilding until the teen reaches full physical maturity.

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HOW IS A FARTLECK?

This type of training, also called "rhythm changes" is to introduce sections interspersed during a shoot in which we run at higher speeds. An example "type" of introducing a fartleck training could be:

- 20-minute progressive warm very soft.

- 6 change the rate of three minutes each, in our current pace of competition in a race of 10 kilometers.

- Insert a pause of 2:30 between each change of pace for 3 minutes. This break must be a very smooth trot, but we must not stop, or walk.

- 15 minutes gentle, to complete the training as "cool down".

must be stressed that these changes of pace are "sprints" outrageous, but simply to begin to accustom our bodies to run in rhythms similar to those that take place in the competition.
Also be aware that those fast sections so you have to make them progressive, and that "it does not" make the first change very quickly and last about the same rate as we keep on shooting. As a training series, you have to go "from strength to strength." Finally

should note that these sessions included fartlecks should last about the same as a normal taxi, ie 1 hour to 1:30 hours, on average, and each change should last from one to five minutes, principle of these trainings "quality" and can grow to eight or ten minutes at most as the weeks go.

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WHAT IS A BLOCK?

is actually a short sequence of training seriously. Let's see an example: 3 x (4 x 500), retrieving 1:30 and 3 minutes. This means that we would first set repetitions within the parentheses (four times 500 meters, recovering 1:30), and then repeat the same sequence twice, totaling three times as detailed in that parenthesis. Between each block of 4 x 500 meters 3 minutos.También recover, if we long series, we can use this format: 2 x (2 x 2,000) meters) recovering 3 and 6 minutes (3 minutes between the two repetitions of 2 km and 6 minutes between the two blocks).

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SERIES STEPPED YOUR FIRST MARATHON

Ever heard of the "ladder series"? No, it is not up and down stairs with series like you're on the track, but to alternate longer runs with shorter. We tell you the "hang of"
ABOVE AND BELOW
ladder series can be of any length, it is immaterial that are long or short. Also called "in pyramids." We will see several short ejemplos.Series: 600 meters + 500 meters + 400 meters + 300 meters + 200 meters, recovered within 2 minutes + 1:45 + 1:30 + 1:15 + 1:00 + 45 seconds. This sequence may be repeated, for example, three times, resting between each bloque.Series five minutes long, 4,000 meters + 3,000 m + 2,000 meters + 1,000 meters, recovered 5 minutes + 4 minutes + 3 + 2 Mintos minutes. This block, of course only do once, and is ideal when preparing evidence maratón.Si marathon or half-steps you want to make long format series an example would be: 2000 meters & 1000 meters + 500 meters, recovering 3 minutes, 2 minutes and a minute respectively. This could repeat the sequence, for example, twice if we are preparing 10 kilómeros cars and three if we are in a period where we have set a target maratón.Una half last possibility is that you make these series of "bottom up", ie starting with the shorter series and ending the longest. Us advise you to do "top down", ie starting with the longest distance and ending with those who prefer more corta.Hay seies also make "pairs", or what is, following the previous example , twice running first 2,000 meters, then twice more than 1,000 meters, and finally 500 metros.Como twice you see, to taste, colors ... Oh, and one last detail: the recoveries can vary them depending on the test you want to make, the longer competition in perspective, the shorter should be the recovery.

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This plan is suitable for those who want to try to finish his first marathon. Any runner who is able to realize this plan, four days a week of training will run with all the guarantees the marathon. Even those who carry out this plan and lose a day's shoot for 5 or 8 weeks, will also be able to finish without problems. And they can do so without suffering too much and experiencing a unique sensation, while above a personal challenge, provided that no mistake in the race strategy. For new marathon that is the key in the marathon. They always want to go faster than your body can be allowed, hence the famous "walls" and the nightmares of the last kms. Another factor that greatly influences the size and weight of the rider. Not be the same result in a person weighing 80 kg and 174 tall, the other weighing 95 kgs and measuring more than 1.85 inches. The weight and height to penalize rather poorly trained marathon runners.
Basic questions for either the plan:
After completing all the training is to perform three abdominal exercises (15 to 25 repetitions each), two lumbar (10 reps) and six to eight Stretching exercises (more concentrated, forcing and for about 15''or 20''in each).
The rhythms of the shooting should be very slow.
You can change the order of days for training, but not by more than two in a row. And in any case join three days.
The weights are essential in preparing the marathon. It is very important to work very specifically the quadriceps (in both eccentric and in concentric), abductors, adductors, calves, the soleus, psoas and biceps femoris. Rendiréis lesionaréis much more and you less. In the week of competition is not done weights. Weights can be replaced by rubber.
is important ankle exercises every week. Fortaleceréis them not ankles, as well mejoraréis efficiency and effectiveness of your stride and diminish the risk of injury much fasciitis, tendonitis and periostitis.
hydration should be at least half a liter of water with minerals every day that you train. And twice as much or if Sudais entrenáis in places where heat and humidity. In addition to other additional liter of water a day.

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APPLICATIONS

trigonometric angle: Suppose
ray beam 0A 0B fixed and mobile. We begin with the two beams coincide. Now, we turn 0B about 0. In each position of rotation determines an angle 0B 0A: the angle A0B. It was agreed to consider the angles generated in a counter clockwise as positive as those generated in the same sense of clockwise and negative, according to the illustration on the right (Fig.1), the angle A0B is positive and the angle A0B 'is negative.

Before starting rotation, 0A and 0B rays coincide, forming an angle of 0 ° (sexagesimal). 0B Turning in the opposite direction clockwise, will generate an increasing angle and when you return to coincide with 0A 0B s and will made a full turn, generating a rotation angle whose measure is 360 °. 0B may continue to rotate and generate an angle of any measure, of what follows that 0A and 0B are the initial and terminal sides, respectively, of an infinity of angles.
unit of measurement of angles: the angles are expressed in degrees, grads or radians.

The sexagesimal system is considered to be the circumference divided into 360 equal parts, and an angle of 1 ° sexagesimal measure that is generated when the rotation in the same direction as the clockwise side of the terminal is of 1 / 360 part of a full turn. Each grade is considered to be divided into 60 equal parts called minutes and each minute into 60 equal parts called seconds. The symbols for these units are:

degrees ° minutes' seconds''

Radian: a radian is defined as the measure of a central angle subtended by an arc with the same length as the radius of the circunferncia . In (Fig.2), the radius r is equal to the arc AB, the angle A0B radians measured 1p.
In the circular system is used as the unit of measure the "radio."
In the system considered proximate to the circumference divided into 400 equal parts called "grads." Each grade has 100 minutes "grads" and every minute has 100 "seconds grads."
Equivalence of an angle in sexagesimal system to move and vice versa. To measure the angles, the most used systems are the sexagesimal and circular. It should know how to convert a given angle from one system to another.
position angle normal:
angle is said is in normal position when its initial side coincides with the positive semiaxis abscissas in a rectangular coordinate axes (Cartesian Plane). And whose apex is at the origin of coordinates (the point where the axes intersect).
In the right figure illustrates a normal position angle, the angle A0B.
Trigonometric Circle:
circle is called trigonometric, or goniometric to the circle whose center coincides with the origin of Cartesian coordinates and whose radius is unity.
On the right you can see a trigonometric circle.

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CIRCLE

1. Find the elevation angle of the sun if a man of 1.75 m. tall, casts a shadow of 82 cm. length on the floor.

2. From a point which is 12 m. soil, an observer obtains a measurement of 53 degrees to the angle of depression of an object found in the soil. About how far is the object point on the ground which is directly under the observer?

3. The string of a comet is taut and forming an angle of 48 degrees with the horizontal. Find the height of the comet with respect the ground, if the line measures 87 m. and the end of the rope is held to 1.3 m. soil.

4. A plane flying at an altitude of 10,000 feet and passes directly over a fixed object on land. A minute later, the depression angle of the object is 42 degrees. Determine the approximate speed of the aircraft.

5. Calculate the width of the street, if an observer on a building, see the other side of it at an angle of 60 degrees from the horizontal.

6. One person is in the window of his apartment which is located at 8m. soil and see the building opposite. Top with an angle of 30 degrees and the bottom at an angle of depression 45 degrees. Determine the height of the building said.

7. A river has two parallel banks. Since the points P and Q from one side, there is a point R on the opposite bank. If the visual form to the address of the bank angle of 40 degrees and 50 degrees respectively, and the distance between points P and Q is 30 meters, determine the width of river.

8. A box is located on a wall so that its lower edge is at a distance of 20 cm. above the eye of an observer situated 2 m from the wall. If the visual angle between the upper and lower edges, respectively, is 10 degrees, what is the height of the picture?

9. A step 6 m. long rests on a vertical wall so that the foot of the ladder is 1.5 m. the base of the wall. What is the angle that the ladder is against the wall and how high the wall reaches the ladder?

10. The lengths of the shadows of two vertical posts are 22 m. and 12 m. respectively. The first pole is 7.5 m. higher than the second. Find the sun's elevation angle and the length of each post.

11. A tree to 12 m. is high on the side of a stream. The angle of elevation of the tree, from a point at 180 m. is 3 degrees. Determine if the stream is above or below the designated point and calculate the level difference.

12. What is the height of a hill, if its elevation angle, taken from its base, is 46 degrees, and taken from a distance of 81 m. is 31 degrees.?

13. On a reef is a beacon whose height is 7.5 m. From a point on the beach can be seen that the angles of elevation to the top and bottom of the lighthouse is 47 degrees and 45 degrees. Calculate the height of the reef.

14. On a horizontal plane, a mast is attached by two wires, so that the straps are on opposite sides. The angles formed by these ties to the ground are 27 degrees and 48 degrees. If the distance enters the wedges is 50 m. How cable has been spent?, what is the height at which the cables are held?

15. From the top of a tower of 200 m. above sea level, the angles of depression of two boats are 47 degrees and 32 degrees respectively. Determine the distance between these boats.

16. A surveyor at C, find two points A and B on opposite sides of a lake. If C is at 5,000 m. of A and 7,500 m. of B and the angle ACB is 35 degrees. What is the width of the lake?

17. Two rangers discovered the same illegal campfire in the direction N 52 ° W and N 55 º E, from their respective positions. The second keeper was 1.93 km. West of the first. If nearest fire warden is the one to go. Which of them has to go and how far to walk?

18. One area is shaped like an isosceles triangle. The base is off a road and has a length of 562 m. Calculate the length of the sides if they form an angle of 23 degrees.

19. A ship leaves a port and travels to the West. At one point rotates 30 degrees North on the West and travel 42 km. further to a point 63 km far. port. How far is the port to the point where he turned the boat?

20. From the top of a tower 300 m. there is a high plane and elevation angle of 15 degrees and a car on the road, on the same side of the plane, with a depression angle of 30 degrees. At the same moment, the car driver sees the plane at an angle of elevation of 65 degrees. If the plane, car, and the observer lie in a vertical plane: calculate the distance between the aircraft and automobiles, also calculate the height at which the plane flies at that time.

21. A triangular area is demarcated by a stone wall of 134 meters, one in front of 205 m. down the road and about 147 m. What angle does the fence with the road?

22. A ladder, whose foot is on the street, forming an angle of 30 degrees with the ground, when its upper end rests on a building on one side of the street, forming an angle of 40 degrees when it meets in a building across the street. If the length of the ladder is 50 m, what is the width of the street?

23. A tree has been broken by the wind so that the two parties are to land a right triangle. The upper part forms a 35 degree angle with the floor, and the distance measured on the ground, from the trunk to the height is 5 m. fall. find the height that was the tree.



24. An observer detects an unidentified flying object statically located at a point space. The observer, using a rangefinder and a sextant, determines that the UFO is at 4460 m. at an elevation angle of 30 degrees. Suddenly the UFO descended vertically to land on the surface. Determine how far the observation point down this object and how far it should go down to touchdown.

25. The angle of one corner of a field in a triangular shape, measures 73 degrees. If the sides, among which is that angle, has a length of 175 feet and 150 feet, determine the length of the third side.

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Trigonometric Trigonometric ratios


The triangle is the key figure metric description for any surface.
Surveyors in purely practical applications, reduce their problems to triangulations.
The theoretical mathematician, in his analysis, often also used this basic polygon
should consider a number of previous definitions:
• A segment x is the mean proportional between two a, b when checked:
·
· Given a point P ay line is called projection of point P on the line to the point P 'defined as the intersection of the perpendicular drawn from P aa and the same line a.
· Projection of a segment MN is on a straight segment M'N ' whose endpoints are the projections of the ends M, N given segment on the line a.
• In a right triangle, sine of an angle is the ratio (the ratio) between the opposite side and the hypotenuse, the cosine of an angle is the relationship between adjacent and the hypotenuse side, the relationship between the sine and cosine an angle (or equivalently the ratio of opposite and adjacent) is the tangent of that angle.
• Although defined in a right triangle, the values \u200b\u200bof sine, cosine and tangent of an angle are fixed values \u200b\u200bthat are fully tabulated in trigonometric tables.
· The reasons sine (sin), cosine (cos) and tangent (tan) and their inverses: cosecant (cosec = 1/sen), secant (sec = 1/cos) and cotangent (cotg = 1/tg) are called trigonometric ratios.




Be the triangle ABC (rectangle in A)
angle
trigonometric ratio 0 º 30 º 45 º 60 º 90 º
Seno 0 0.5 0.707 0.866 1
Cosine 1 0.866 0.707 0.5 0
Tangent 0 .577 1 1, 73 oo

Theorem: Theorem
leg.
In any right triangle verifies that one leg is a mean proportional between the hypotenuse and the projection of that leg on the hypotenuse:

height theorem.
In any triangle, the height is a mean proportional between the two segments that divides the hypotenuse:

Pythagorean Theorem.
In any right triangle is true that the square of the hypotenuse equals the sum of the squares of the legs:
a2 + b2 = c2
From the definitions of the trigonometric ratios follows:
b = a sin B = a
cos C c = a cos B = a sin C
tg B b = c, c = b tg C

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Sources

Historians agree that it was the Greeks before Socrates initiators of trigonometry. Thales of Miletus, one of the Seven Sages of Greece, is credited with the discovery five geometric theorems and their participation in the determination of the heights of the pyramids of Egypt using the relationship between angles and sides of a triangle. Hipparchus, Greek astronomer and mathematician notable, systematized these concepts in a table of trigonometric chords that are now the basis of modern trigonometry. For his work is considered the father or founder of trigonometry.
is considered to Hipparchus (180-125 BC) as the father of trigonometry mainly for his discovery of some of the relationships between sides and angles of a triangle. Also contributing to the consolidation of trigonometry Claudius Ptolemy and Aristarchus of Samos who applied it in his astronomical studies. In 1600, professor of mathematics at Heidelberg (the oldest university in Germany) Pitiscus Bartholomew (1561-1613), published a text with the title of trigonometry, which develops methods for solving triangles. The French mathematician François Viète (1540-1603) made important contributions to finding multiple angle trigonometric formulas. Trigonometric calculations received a boost thanks to the Scottish mathematician John Napier (1550-1617), who invented logarithms in the early seventeenth century. In the eighteenth century, the mathematician Swiss Leonhard Euler (1707-1783) made a science of trigonometry in addition to astronomy, to turn it into a new branch of mathematics. Originally
, trigonometry is the science whose object is the numerical (algebraic) of the triangles. The six key elements in any triangle are its three sides and three angles. When you know three of these elements, provided that at least one being the one hand, teaches trigonometry to solve the triangle, that is, to find the other three elements. In this state of trigonometry defined the trigonometric functions (sine, cosine, tangent, etc.) Of an acute angle in a triangle rectangle, as the ratios between two sides of the triangle, the domain of definition of these functions is the set of values \u200b\u200bthat can take the angle [0, 180].
HOWEVER, the study of trigonometry does not limit its application to the triangles, geometry, navigation, surveying, astronomy, but also for the mathematical treatment in the study of wave motion, vibration, sound, alternating current, thermodynamic atomic research, etc.. To achieve this, we must broaden the concept of a function trigonometric function of a real variable, rather than simply a function of angles.

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trigonometry trigonometry, What is?

The basic problem of trigonometry is something like this:

is near a wide river and need to know the distance to the other side, say to the tree marked in the drawing by the letter C (for simplicity, ignore the 3 rd dimension). How to do it without crossing the river?

The usual way is as follows. Drive two stakes into the ground at points A and B and with a tape measure the distance c between them (the "base").

An old surveyor's telescope (theodolite).
Then remove the post from point A and replace it with a surveyor's telescope as the one shown here ("theodolite"), with a plate divided into 360 degrees, check the direction ("azimuth") that points the telescope. Pointing the telescope to the tree first and then to the pole B, measures the angle A of triangle ABC equal to the difference between the numbers that you have read the azimuth plate. Replace the post, move the theodolite to point B and measured in the same way the angle B.
length c of the base and the two angles A and B are all you need to know the triangle ABC, enough, for example, to build a triangle of the same shape and same size, in a more convenient place. Trigonometry (trigon = triangle) at first was the art of calculating the lost information by simple calculation. Given sufficient information to define a triangle, trigonometry is used to calculate the other dimensions and angles.

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What is trigonometry?

Trigonometry is a branch of mathematics of ancient origin, whose etymological meaning is "the measurement of triangles." It derives from the Greek word τριγωνο "triangle" + μετρον "measure"

in principle Trigonometry is the branch of mathematics that studies the relationships between angles and sides of triangles. For this it uses the trigonometric ratios, which are frequently used in engineering calculations. Overall, trigonometry is the study of the sine, 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 the geometry of space.

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