Trigonometry in everyday life
Introduction.
A branch of mathematics that studies the relationship between the sides and the angles of the triangles, the properties and applications of the trigonometric functions of the angles. The two basic branches of trigonometry are flat trigonometry, which deals with graphics contained in planes and spheres, and processes a triangle that is part of the surface of a sphere.
The first applications of trigonometry were in the navigation, geodesy and astronomy fields, and the main problem was to determine unattainable distances, such as distance from earth to the moon or non -measured distances. Direct, you can find other applications of trigonometry in physics, chemistry and almost all branches of engineering, especially in the study of periodic phenomena, such as alternate acoustic currents.
Developing.
Trigonometry is a subdivision of mathematics that is responsible for calculating the elements of a triangle. To this end, he dedicated himself to studying the relationship between the angles and the sides of the triangles, which can also be closely related to everyday life. It is the branch of mathematics that studies the relationship between the sides and angles of the triangles, therefore, the functions associated with the angles, called trigonometric functions, can also be called circular functions: sinus, cosine, tangent, dry. Trigonometry has innumerable applications in various fields of science;in one way or another in all fields of mathematics;In physics, in astronomy, etc.
Historically, the ancient Egyptians and the Babylonians already knew the theorems of the proportions of the sides of the similar triangles, but the prehellenic societies lacked the notion of a measure of the angle and therefore, the sides of the triangles were studied to their extent, a field that could be called trilaterometry.
Babylonian astronomers brought detailed records on the exit and set of stars, movement, planets and solar and lunar eclipses, all of which requires familiarity with the angular distance measured on the celestial sphere. Some have even affirmed that the Babylonians had a drying table. The Egyptians, in the second millennium before Christ, used a primitive form of trigonometry, for the construction of pyramids.
It is mainly used for navigation and astronomy, studies spherical triangles, that is, figures formed by arches of the largest circumference contained in the surface of a sphere. A spherical triangle, such as a flat triangle, has six elements, namely three sides A, B, C and three corners A, B and C. However, the sides of a spherical triangle are angled, not linear. And, since they are arches of the largest circumference of a sphere, their measures are given by the corresponding central angles.
A spherical triangle is defined by giving three of the six elements, because, as in flat geometry, there are formulas that can associate different parts of a triangle so that they can be used to calculate unknown elements. The spherical triangle method is very important for the theory of stereo projection and geodesy. It is also the basis of astronomical calculations. For example, use the solution of a so -called astronomical triangle to find the latitude and length of a point, the time of day, the position of a star and other sizes.
The concept of triangular angle is the basis of trigonometry research. Create a triangular angle with a rotation radius. The radio was initially considered consistent with OA. OB radio turns to its final position. If the angle generated and its radius are turned antihoranously, the angle and its magnitude are positive;If the turned angle is turned in a schedule, the angle and its magnitude are negative. Two triangles are equal if they have the same rotation and the same direction.
Cateto B rectangle triangle and its cateto parts is resolved to find its sides, angles and their area. To know its sides, the Pythagorean theorem is used: C² = A² + B² To know its angles, trigonometric functions are used: and to know its area the formula is used:
Application of trigonometry in everyday life
Astronomers use triangulation (triangulation) to calculate the distance to nearby stars. In geography, it is used as the distance between the reference points. Trigonometry is particularly important in architecture because it allows architects to calculate distances and forces related to diagonal elements. Of the six basic trigonometric functions, sinus, cosine and tangent are the most important for architecture because they make it easier for architects.
There are many applications of triangulation techniques: triangulation techniques (determination of the position of a point, distance or digital air measurement), for example, to measure distances of nearby stars and satellites. Trigonometry makes many contributions in our society, such as the construction of houses or buildings and the different measures that must be taken. Trigonometry is very useful in civil engineering for precise calculations.
Trigonometry in topography.
Science that studies the set of principle and the process of graphically representing the surface of the earth and its forms and details;natural and artificial. Trigonometry is an important part of the terrain, because it is the base, without which it is impossible to know the distance, coordinates, angular measures, etc.
Thanks to them today, the location on the ground can use the following positioning systems to determine the position of objects, people, vehicles or ships: GPS for positioning, distance or inclination. Waiting on the road
conclusion.
Over time, a lot of characters have dedicated their lives to contributing to the calculations that help us and lead us to find exact answers and results, and thus discover the causes of phenomena and events in human history. One of the most important points in mathematics is to seriously emphasize that trigonometric functions are values without units that depend on the size of the angle.
If the vertices of the vertices of the rectangular coordinate plane coincide with the origin, and its initial edges coincide with the positive part of the X axis, the angle that is in the rectangular coordinate plane is called a normal position. These functions were created from flat and spherical trigonometric functions, and then refined and implemented what we now call trigonometric functions. It is necessary to clarify its importance because it is part of mathematics and the basis for the development of certain operations. . Calculate to obtain the result of the objective set.
BIBLIOGRAPHY
- Cuellar Carvajal, Juan Antonio (2005). Mathematics II for Baccalaureate (1.ª edition). Mexico: McGraw-Hill Editorial.
- Baley, John D.;Sarell, Gary (2004). Trigonometry. (3.ª edition). Mexico: McGrllal Hornsby (2006). Trigonometry. (1.ª edition). Mexico: Pearson Editorial.
- Pepper Prieto, Julio;Acosta Argüello, Vicente;Ramos Zarco, Octavian;Villegas C, Guillermo (2006). Mathematics III. (1.ª edition). Mexico Pearson Prentice Hall.
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