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real life applications of trigonometry

Maths Project

haney chandra

on 11 September 2013

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Transcript of real life applications of trigonometry

By Haney
Roll No: 17
Real Life Applications of Trigonometry-A Journey
Application Of Trigonometry
Let's explore areas where this science finds use in our daily activities and how we can use this to resolve problems we might encounter. Although it is unlikely that one will ever need to directly apply a trigonometric function in solving a practical issue, the fundamental background of the science finds usage in areas which is passion for many.
You cannot separate architecture from trigonometry, which is critical for curving surfaces in building materials such as steel and glass. The science is used to find the heights of buildings, or create dimensional objects to use in buildings. Trigonometry is used to make demarcations for cubicles in an office building. It is useful when designing a building to predetermine geometrical patterns and how much material and labor will required in order to erect a structure. In fact the flat panels and straight planes in the building are at an angle to one another and the illusion is that of a curved surface. Neat huh!When the building is erected, it will not only be strong, it will have accurate measurements.
Several imaging technologies that apply the concepts of trigonometry find usage in medicine. The advanced scanning procedure, the practical application of medical techniques such as CAT and MRI scanning, in detecting tumors and even in laser treatments, etc. use the sine and cosine functions. It's greatest application is in orthopedics.
Medical Techniques
Trigonometry was born as a complement to astronomy. The foundations of trigonometry allowed astronomers to determine all sorts of information about stellar bodies, including distances, mass, orbits and speed. Trigonometric functions give us the ability to figure out these things through inference since we do not have the capability to simply go measure it. Because astronomical bodies exist on much larger scales than things on earth, mathematics is the only way to deal with them practically. The depth of our knowledge would be much less without trigonometry to help fill in the gaps.
Trigonometry is a scary word for many adults and students alike. It conjures up visions of complicated equations, functions, graphs and geometrical shapes. However, Trigonometry has many applications in the modern world. Without it, many modern industries and sciences would simply not exist. By learning a few "real world" applications of trigonometry, one can see just how important and indispensable this branch of mathematics really is to our world. What began as the computational side of geometry blossomed into a full science in and of itself. So we must not we afraid of it because wherever we'll go
Digital imaging is another real life application of this marvelous science. Computer generation of complex imagery is made possible by the use of geometrical patterns that define the precise location and color of each of the infinite points on the image to be created. The image is made detailed and accurate by a technique referred to as triangulation. The edges of the triangles that form the image make a wire frame of the object to be created and contribute to a realistic picture.
Digital Imaging
Trigonometry plays a huge role in all varieties of physics. For example, consider that radio, microwave, and electromagnetic waves are all measured and graphed with trigonometric functions such as sine and cosine. Physics concerns itself greatly with three-dimensional space. Mathematics is critical being able to determine values and help identify the nature of something in the space it exists in. Trigonometry is used so much in physics that it is as prevalent as simple addition and subtraction for the average person.
Music Production

Trigonometry is an area of mathematics that probes the property of triangles. It is used in satellite systems and astronomy, aviation, engineering, land surveying, geography and many other fields. Precisely, trigonometry is a branch of mathematics that deals with triangles, circles, weaves and oscillations.
What is Trigonometry ?
The techniques in trigonometry are used for finding relevance in navigation particularly satellite systems and astronomy, naval and aviation industries, oceanography, land surveying, and in cartography (creation of maps).
Trigonometry is a subset of mathematics that deals with right triangles and their graphs. There are six primary graphs or functions in trigonometry, but they all stem from the sine, cosine and tangent equations. These three functions are the proportions of the sides of a right triangle to the angles. In addition, the trigonometric formulas relate to circles and graphs making them useful to many different subsets of math and science.
Sound engineers who work in advancing computer music, and hi-tech composers have to apply the basic law of trigonometry such as the cosine and sine function. Music waves patterns are not as regular as sine and cosine function, but it is still helpful in developing computer music. A computer cannot obviously listen to and comprehend music as we do, so computers represent it mathematically by its constituent sound waves. And this means that sound engineers and technologists who research advances in computer music and even hi-tech music composers have to relate to the basic laws of trigonometry. The simplest sounds called pure tones are represented by:
f(t)=A sin (2 pi w t)
Ptolemy used trigonometric tables for navigation as early as the first century. Christopher Columbus kept these on hand during his voyages to the New World for the same purpose. Trigonometry came first to the sky before geography.
During the 15th century, Christian Spaniards, Muslim Moors and Sephardi Jews worked together to translate the works of trigonometry and algebra to Castillan and Latin. This is how Columbus, De Gama and Magellan managed to sail across oceans.
Still today, seafarers use Mercator projection maps because it uses right angle latitudes and longitudes. This is needed for astro-navigation because it requires trigonometry. But pilots prefer Lambert projection that is closer to the great-circle navigation, the path taken by radio-navigation signals.
The ability of trigonometry to help us understand positions on a spherical-shaped planet make it critical to modern conveniences such as global navigation and sonar. Surveyors use trigonometric functions when making maps and analyzing areas for construction projects.
Ge graphy
Triangulation, which is an application of trigonometry, is also used in satellite navigation systems. In astro-navigation, one uses spherical trigonometry, which is not the same as the plan trigonometry like Pythagorus.
For instance, a pilot taking off from JFK airport in New York will have to know which angle to take off from and when to turn at a certain angle in the sky in order to reach Heath row airport in London.
Who said studying math has only an academic value! Need other reasons to know how formulae in trigonometry make life easier for you? Now we all use patterns and symmetry for relating objects around us. For instance there is a need for harmony and symmetrical agreement even if you are just redecorating your home. You need to be sure about angles and positioning when deciding lighting arrangements. And although you won't need to write out sine formulae for this one, you will still be using the basic laws of triangles in deciding the best angle to show off that trendy lamp on your study table!
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