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Trigonometría

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carmen campos

on 22 June 2015

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Transcript of Trigonometría

Trigonometry aplications
Surveying:
Important characters
Menelaus of Alexandria

Greek mathematician. He cultivated astronomy and geometry in Alexandria and Rome. He made a systematic study of the properties of spherical triangles (theorems of Menelaus), which constitute the basis of spherical trigonometry.


Relations between trigonometric reasons
Consider the sinA = a / c and cos A = b / c, if we add the squares and we consider the Pythagorean theorem a2 + b2 = c2

The fundamental relationship of trigonometry is obtained
sen2A + cos2 A = 1
If we divide both sides of the equation by cos2A a second equality is obtained:
A = 1 + tg2 sec2A
If we divide both sides of the equation by sin2 A second equality is obtained
A = 1 + cotg2 cosec2A
Trigonometric
Reasons
Origin
The Babylonians and Egyptians were the first to use the angles of a triangle and trigonometric ratios for measurements in agriculture and to build pyramids. It was developed more to the study of astronomy.

After studying trigonometry he came to Greece. Later it spread to India and Arabia (for astronomy). From Arabia it spreads across Europe. There is separated from astronomy to become an independent branch of mathematics

Trigonometría
A late eighth century Arab astronomers worked with the sine function and the late tenth century had completed the sine function and the other five functions. They also discovered and proved fundamental theorems of trigonometry.

A mid-seventeenth century Newton found the series for sin x, series for cos x and tan x.


In the eighteenth century, Leonhard Euler proved that the properties of trigonometry were the result of the arithmetic of complex numbers and further defined the trigonometric functions using exponential expressions with complex numbers.


Edmund Gunter

English mathematician. His principal works dealt trigonometry and logarithmic calculation. He introduced the cosine terms and cotangent, he developed the logarithmic arithmetic.


Rheticus

German mathematician and astronomer. He first linked trigonometric functions of angles and produced one of the best trigonometric tables of his time.
Leonhard Euler

Leonhard Euler was a respected mathematician and physicist. He is considered the leading mathematician of the eighteenth century and as one of the greatest of all time.

Ejercicios
1.Calcular la altura del arbol con los siguentes datos:



2. Resuelve la siguiente identidad trigonométrica:
Used sources
http://trigonometriasonia.blogspot.com.es/2008/10/historia-de-la-trigonometra.html

http://trigonometriadidactica10b.blogspot.com.es/2011/10/personajes-que-aportaron-la_23.html



In surveying trigonometry is used to measure angles.
Astronomy
Astronomy is a science which studies the structure, composition and process of the stars and his laws of motion.
20m
h
60°
1+tgx
------
secx
= senx + cosx
Marina Lirola
Eva García
Antonio Fco Jódar
Carmen Campos

Quadrants and signs of the trigonometric reasons
senx= +
cosx= +
tgx= +
I Quadrant
II Quadrant
senx= +
cosx= -
tgx= -
III Quadrant
senx= -
cosx= -
tgx= +
IV Quadrant
senx= -
cosx= +
tgx= -
Full transcript