An Introduction to the Trigonometry and Mathematics in Everyday Life

Trigonometry utilizes the fact that the proportions of sets of sides of triangles are functions of the angles. The basis for mensuration of triangles is the right-angled triangle. The term trigonometry essentially means the measurement of triangles. Trigonometry is a branch of mathematics that developed from simple measurements. A theorem is the most important concept in all of primary mathematics. It was the motivation for a wealth of advanced mathematics, such as Fermat's Last Theory and the theory of Hilbert Space.

The Pythagorean Theorem asserts that for a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. There are many ways to prove the Pythagorean Theorem. An especially 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 like Egypt, Mesopotamia, India, and China? What did these ancient cultures know about the theorem? Where was the theorem used in their cultures? In "Geometry and Algebra in Ancient Civilizations," the author discusses the original discoverer of the Pythagorean Theorem. He quotes Proclus, a commentator on Euclid's elements, saying that, "if we listen to those who wish to recount the ancient history, we may find some who attribute this theorem to Pythagoras and assert that he sacrificed an ox in honor of his discovery." If this statement is taken as fact, it is highly improbable because Pythagoras opposed animal sacrifice, particularly of cattle. If this saying is considered merely a legend, it is easy to deduce how such a story could have started.

Possibly the initial version of the story claimed something similar: he who discovered the famous figure sacrificed a bull in honor of his discovery. Van der Waerden continues to comment that he believes the initial discoverer was a priest, before the time of Babylonian texts, who was allowed to sacrifice animals and also happened to be a mathematician. This question can never be definitively answered, but there is evidence that cultures utilized the theorem before the time of Pythagoras. The theorem is useful in everyday life. For example, at a certain time of day, the sun's rays can cast a three-foot shadow off a four-foot flag pole. Knowing these two lengths, and the fact that the pole forms a ninety-degree angle with the ground, allows one to calculate the distance from the end of the shadow to the top of the pole without measuring.

The first step is to substitute the given information into the formula. Now you can ascertain the length of the third side, which is five feet. Trigonometry is fundamentally the study of the relationship between the sides and angles of right triangles. Knowing how to utilize these relationships and ratios is absolutely essential for virtually everything. It might not seem like it, but trigonometry is used nearly everywhere. Another example of the importance of the theorem is the world orb symbol, which represents engineering studies. Although there are several components to this symbol, the Pythagorean theorem lies correctly at the center, because much of engineering, mensuration, logarithms, etc., is based on trigonometric functions.

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