## 16 May

# Trigonometry

The most basic of shapes in terms of simplicity is arguably the triangle. Trigonometry comes from the Greek words trigonal and metron which means triangle measure. In mathematics, trigonometry is a branch that focuses on the relationship between the length of the triangle sides and its associated angles. The subject origin can be traced back to when scientists started studying geometrical applications in astrological sciences. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. In particular, 3rd-century astronomers first noted that the ratio of the lengths of two sides of a right-angled triangle depends only on one acute angle of the triangle. These dependencies are now called trigonometric functions.

There are three basic functions in trigonometry which forms the basis of all trig functions and applications. These are the Sine function, Cosine Function, and the Tangent function. The Tangent function can be expressed as a quotient of the Sine and Cosine functions. These three all relate to the Right-angled triangle with sides being assigned specific designations. These are; the opposite, the adjacent and hypotenuse. The correlation of the sides of the triangle to the internal angles enables the calculation of any missing values.

Application of trigonometry is very helpful in determining aspects of the universe that cannot be feasibly measured. For example, the distance from the sun cannot be directly measured but, with trigonometry, it is very possible. Scientists simply measured the angle of the sun from a random point and the distance from that point to another point perpendicular to the sun. The trigonometry functions work hand in hand with other proven theories such as Pythagoras’s. This breakthrough makes research in fields such as astrology pretty simple or at least feasible.

Trigonometry can be applied to any triangle regardless of its internal angles. Mathematical operations in trigonometry are complemented by what is known as ‘identities’ which give the relationships between the various trigonometric functions. It is important to understand the formulation of the basic three functions before attempting to understand any other trig functions such as the cosec function. This enables students to formulate any required trigonometry function on-demand without necessarily committing them to memory.

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