Trigonometric Ratios

Trigonometry is the study of triangles. "Tri" is Ancient Greek word for "three", "gon" means "side", "metry" means "measurement". Together they stand for "measuring three sides". The primary object of the science of Plane Trigonometry is to develope a method of solving plane triangles. A plane triangle has three sides and three angles, and supposing the magnitudes of any three of these six parts to be given, one at least of the three given parts being a side, it is possible, under certain limitations, to determine the magnitudes of the remaining three parts; this is called solving the triangle.

We have learned from elementary geometry that a triangle is determined when we know any three of its parts (sides and angles), at least one of them being a side. These data enable us to construct the triangle; but elementary geometry does not teach us how to calculate the remaining parts. The reason is that sides and angles are expressed in different units. It is, therefore, desirable to measure angles not only in degrees (or radians), but also by means of sides, or rather by means of ratios of sides, called trigonometric ratios.

In every brach of Higher Mathematics, whether Pure or Applied, a knowledge of Trigonometry is of the greatest Value. Trigonometry starts by examining a particularly simplified trangle, the right-angled triangle. More complex triangles can be built by joing right-angled triangles together. More complex shapes, such as squares, hexagons, circles and ellipses can be constructed from two or more triangles. Ultimately the universe we live in, can be mapped through the use of triangles. For instance, the Ancient Greeks were able to use trigonometry to calculate the distance from the Earth to the Moon.

Before dwelling upon the topic of trigonometric ratios, it would be convenient to introduce the notion of "angle" in Trigonometry problems .

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