Trigonometry uses the fact that ratios of pairs of sides of triangles are functions of the angles. The basis for mensuration of triangles is the right- angled triangle. The term trigonometry means literally the measurement of triangles. Trigonometry is a branch of mathematics that developed from simple measurements.

A theorem is the most important result in all of elementary mathematics. It was the motivation for a wealth of advanced mathematics, such as Fermat's Last Theorem and the theory of Hilbert space. The Pythagorean Theorem asserts that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. There are many ways to prove the Pythagorean Theorem. A particularly simple one is the scaling relationship for areas of similar figures.

Did Pythagoras derive the Pythagorean Theorem or did he piece it together by studying ancient cultures; Egypt, Mesopotamia, India and China? What did these ancient cultures know about the theorem? Where was the theorem used in their societies? In "Geometry and Algebra in Ancient Civilizations", the author discusses who originally derived the Pythagorean Theorem. He quotes Proclos, a commentator of Euclid's elements, "if we listen to those who wish to recount the ancient history we may find some who refer this theorem to Pythagoras, and say that he sacrificed an ox in honor of his discovery". If this statement is considered as a statement of fact, it is extremely improbable, for Pythagoras was opposed to the sacrifice of animals, especially cattle. If the saying is considered as just a legend, it is easy to explain how such a legend might have come into existence. Perhaps the original form of the legend said something like he who discovered the famous figure sacrificed a bull in honor of his discovery.

Van der Waerden goes on to comment that he believes the original discoverer was a priest, before the time of Babylonian texts, who was...

...Intro:
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies. It is also the foundation of the practical art of surveying.
Trigonometry basics are often taught in school either as a separate course or as part of a precalculus course. Fields that use...

...The Way Trigonometry is used in Astronomy
By: Joanna Matthews
Practical Applications of Advanced Mathematics
Mrs. Amy Goodrum
July 15, 2003
Abstract
This report is about how trigonometry is used in Astronomy. Even though trigonometry is applied in many areas, such as engineering, chemistry, surveying, and physics, it is mainly used in astronomy Trigonometry is used to find the distance of stars, the distance from one planet to...

...Application of Trigonometry in Real Life Situation
Mathematics is a subject that is vital for gaining a better perspective on events that occur in the natural world an in real life situation. A keen aptitude for math improves critical thinking and promotes problem-solving abilities. One specific area of mathematical and geometrical reasoning is trigonometry which studies the properties of triangles. In some of the fields such as architecture, astronomy , biology,...

...Running Head: History of Trigonometry
History of Trigonometry
Rome Fiedler
History of Mathematics 501
University of Akron
April 29, 2012
History of Trigonometry: An Introduction
Trigonometry is useful in our world. By exploring where these concepts come from provides an understanding in putting this mathematics to use. The term Trigonometry comes from the Greek word trigon,...

...Real Life Applications of Trigonometry
A. Importance/Application of Trigonometry in General
Fields that use trigonometry or trigonometric functions include astronomy (especially for locating apparent positions of celestial objects, in which spherical trigonometry is essential) and hence navigation (on the oceans, in aircraft, and in space), music theory, acoustics, optics, analysis of financial markets, electronics,...

...rigonometric Ratios of Special Angles
We have already learnt that trigonometry is the study of relationships between the sides and angles of a triangle. The ratios of the sides in a right triangle with respect to its acute angles are called trigonometric ratios of the angle. The angles and are useful angles in trigonometry, and their numerical values are easy to remember.
When two angles add up to 900, then any one angle is the complement of the other....

...consequently known as "the father of trigonometry."[3]
Sumerian astronomers introduced angle measure, using a division of circles into 360 degrees.[4]They and their successors the Babylonians studied the ratios of the sides of similar triangles and discovered some properties of these ratios, but did not turn that into a systematic method for finding sides and angles of triangles. The ancient Nubians used a similar methodology.[5] The ancient Greeks transformed...

...geometry and trigonometry now that there are satellites? Has the function of geometry and trigonometry in triangulation and navigation changed since satellites were built?
IB MATH
Candidtate name: Tristan Stevenson
Candidate Number: dwq773 (001366 – 016)
School: Prem tinsulalonda International School
November 14, 12
Word Count:2090
Abstract:
This essay examines the question: How does GPS...

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