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Trigonometry and application in the economy

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Maria Franco

on 9 June 2015

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Transcript of Trigonometry and application in the economy

The sine and cosine functions are much needed in modeling cyclical trends such as seasonal variation in demand for certain items, they are also very necessary to solve problems of daily life , financial , economic and statistical issues .

Applying trigonometry to economy

What is trigonometry ?
Trigonometry uses 3 types of measurement units ( Radian ,Degree and Gradian ) but also uses three trigonometric funtions ( sine, cosine and tangent) and likewise their reciprocal ( Cotangent , secant and Cosecant ) .
How do you use it?
Trigonometry is part of mathematics that is responsible for calculating the elements of triangles.
This should study the relationships between the angles and sides of triangles.


They are essential to determine the seasonal variation in demand for certain items. in this case the cyclical behavior is very important in the business world.
Applications
Examples
References
Trigonometry and application in the economy
Sydsaeter, Knut, and Peter Hammond. Matemáticas Para El Análisis Económico. Estados Unidos: Pearson Educación, September 9, 1996. Print.
Warner, Stefan, and Steven R. Costenoble. "Trigonometric Functions and Calculus for Liberal Arts and Business Majors." Trigonometric Functions. Real World Wide Web, Mar. 1996. Web. 16 May 2015. (http://www.zweigmedia.com/ThirdEdSite/trig/trigintro.html)
Jiménz, Giovanna J. "15 Funciones Trigonometricas En La Vida Cotidiana. Notafrancesco Doc." 15 Funciones Trigonometricas En La Vida Cotidiana. Notafrancesco Doc. N.p., n.d. Web. 16 May 2015. <http://www.academia.edu/6123267/15_Funciones_trigonometricas_en_la_vida_cotidiana._Notafrancesco_doc>.
Waner, Stefan, and Steven R. Costenoble. "This Section: 1. Modeling with the Sine Function." The Trigonometric Functions. N.p., n.d. Web. 24 May 2015. <http%3A%2F%2Fwww.zweigmedia.com%2FThirdEdSite%2Ftrig%2Ftrig1.html>.
Salazar, Bryan. "VARIACIÓN ESTACIONAL O CÍCLICA." Ingenieria Industrial Online. Ingenieriaindustrialonline, n.d. Web. 27 May 2015. <http%3A%2F%2Fwww.ingenieriaindustrialonline.com%2Fherramientas-para-el-ingeniero-industrial%2Fpron%C3%B3stico-de-ventas%2Fvariaci%C3%B3n-estacional-o-c%25C3%25ADclica%2F>.
Lina Franco 10A
The following graph, which shows the approximate average daily high temperature in New York's Central Park.
Each year, the pattern repeats over and over, resulting in the following graph. Here, the x-coordinate represents time in years with x = 0 representing August 1, while the y-coordinate represents the termperature in ºF. This is an example of cyclical or periodic behavior.
A clear example is the temperature of NYC and how it affects the market .
The following graph suggests a cyclical behavior in employment at securities firms in the United States.
We can see that we have the same seasonal fluctuations in temperature in Central Park, there are seasonal fluctuations in demand for surfing equipment , swimwear , snow shovels , etc . since the temperature change, it also chage the demand of the products sold under the temperature and in the case of US, the behavior stations .
Other Examples.
Imagine a bicycle, wheel whose radius is one unit, with a marker attached to the rim of the rear wheel, as shown in the following figure.
As the wheel rotates, the height h(t) of the marker above the center of the wheel, fluctuates between 1 and +1.The faster the wheel rotates, the faster the oscillation. Let us now choose our units of measurement so that the wheel has a radius of one unit. Then the circumference of the wheel (the distance all around) is known to be 2, where π= 3.14159265.... When the outer edge of the wheel has traveled this distance, it has gone through exactly one revolution, and so it is back where it started. Thus, if, at time t = 0 the marker started off at position h(0) = 0, then it is back to zero after one revolution. If the cyclist happens to be moving at a speed of one unit per second, it will take the bicylce wheel 2 seconds to make one complete revolution, and so the wheel is back where it started atfer that time.
Conclusions

Trigonometry to be in all areas of life It gives us in every university career, the possibility of solving different problems ,in the economy it gives us the possibility of finding the results for financial problems and also assess the highlights in the sale of a product thus generating more positive results.
Formulas
Example applying a forecast or Cyclic Variation Seasonal,
CAROLA stationery distributor wants to sell in 2015 an amount of 12,000 school kits .
Determine prognosis per quarter from seasonal variation model , considering the following information about the behavior of sales:






Solution
The first step is to determine the overall average sales for this , we must add the total sales and divide by the number of quarters.

Then we proceed to calculate the average sales for each period , in this case of each period have only one thing will exist in practice exercises in which each period (eg quarter I) have lots of historical information, eg historical information I quarter of five years . As mentioned , for this case we are not averaging necessary since we only with data of each quarter , for that reason we proceed to calculate the seasonal index for each period.


Considering that you want to sell a total of 12,000 kits 2015 , calculate the overall sales for the year , for it will divide this amount by the number of quarters.


Since we have the overall sales of the year and we want to predict the seasonal index for each quarter , it is time to determine the prognosis for 2015 quarter .

Taken from:http://www.sosmath.com/trig/Trig2/trig2/trig2.html
Taken from:http://www.ingenieriaindustrialonline.com/herramientas-para-el-ingeniero-industrial/pronóstico-de-ventas/variación-estacional-o-c%C3%ADclica/
Taken from:http://www.wikimatematica.org/images/9/98/Grafica.svg.png
Taken from:National Weather Service/The New York Times, January 7, 1996, p. 36.
Taken from: http://www.zweigmedia.com/ThirdEdSite/trig/trig1.html
Taken from: http://www.pac.com.ve/images/stories/publicaciones/educacion/cuatroestacionesano-g-080914.jpg and http://www.guarderiasalamanca.com/blogs/wp-content/uploads/2013/05/cancion-estaciones-en-ingles.jpg
Taken From: Securities Industry Association/The New York Times, September 1, 1996, p. F9.
Lina Franco 10A
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