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...

...Trigonometry (from Greek trigōnon "triangle" + metron"measure"[1]) is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies.[2] It is also...

...Trigonometry (from Greek trigōnon "triangle" + metron "measure"[1]) is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical...

...Right Triangle TrigonometryTrigonometry is a branch of mathematics involving the study of triangles, and has applications in fields such as engineering, surveying, navigation, optics, and electronics. Also the ability to use and manipulate trigonometric functions is necessary in other branches of mathematics, including calculus, vectors and complex numbers. Right-angled Triangles In a right-angled triangle the three sides are given special names. The side...

...ANSWER:
8-4 Trigonometry
Express each ratio as a fraction and as a decimal to the nearest
hundredth.
1. sin A
3. cos A
SOLUTION:
The cosine of an angle is defined as the ratio of the adjacent side to the
hypotenuse. So,
ANSWER:
SOLUTION:
The sine of an angle is defined as the ratio of the opposite side to the
hypotenuse. So,
4. tan A
ANSWER:
2. tan C
SOLUTION:
The tangent of an angle is defined as the ratio of the opposite side to the
adjacent side. So,...

...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 trigonometry into an ordered science.[6]
Classical Greek mathematicians (such as Euclid and Archimedes) studied the properties of chords and inscribed angles in circles, and proved theorems that are equivalent to modern trigonometric...

...Trigonometry is a field of mathematics first compiled by 2nd century BCE. Greek mathematician Hipparchus. The history of trigonometry and of trigonometric functions follows the general lines of the history of mathematics.
Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics (Rhind Mathematical Papyrus) and Babylonian mathematics. Systematic study of trigonometric functions begins in Hellenistic mathematics, reaching India as...

...Spherical trigonometry
Spherical trigonometry is that branch of spherical geometry which deals with the relationships between trigonometric functions of the sides and angles of the spherical polygons (especially spherical triangles) defined by a number of intersecting great circles on the sphere. Spherical trigonometry is of great importance for calculations in astronomy, geodesy and navigation.
The origins of spherical trigonometry in...

...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,...

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