16 May Trigonometry
The most basic of shapes in terms of simplicity is arguably the triangle. Trigonometry meaning 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 Origin of Trigonometry
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.
Basic 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.
The Importance of Trigonometry in Science
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.
Trigonometric Identities and Their Applications
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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FAQs:
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, especially right-angled triangles.
What is the origin of trigonometry?
Trigonometry originated in the Hellenistic world during the 3rd century BC, initially emerging from the study of astronomy and geometry.
What are the basic trigonometry formulas?
The three basic trigonometry functions are:
Sine (sin)
Cosine (cos)
Tangent (tan)
These relate to the ratios of the sides of a right-angled triangle.
Why is trigonometry important in mathematics?
Trigonometry helps solve problems related to angles and distances that are difficult to measure directly, especially in fields like astronomy and engineering.
Where is trigonometry used?
Trigonometry is used in many fields, including astronomy, physics, engineering, and even in computer graphics. It is essential for measuring distances and angles in situations where direct measurement is not possible.
How can I understand trigonometry better?
To understand trigonometry better, focus on mastering the basic functions and formulas first. Using visual aids like diagrams and practicing problems will also help.