Trigonometry is a fascinating subject. Everything from the trigonometric ratio tables with their irrational numbers to the history of the origin of this branch of Mathematics is surrounded by interesting facts. Right since its inception, trigonometry caught the imagination of mathematicians and philosophers alike. Its concepts and ratio tables could be used to measure the sizes and distances of astronomical and Hellenistic bodies, as well as structures on the earth. Projections for upcoming structures could be made with great accuracy thanks to the simple trigonometry formulae. Although the ancient studies of trigonometry are credited to the Greeks, Indian Mathematicians of yore such as Aryabhatta are known to have studied the ‘sine’, one of the primary trigonometric ratios.
Here are some facts about trigonometry:
Aryabhatta proposed the first table of sines in his work
In the Aryabhatiya, Aryabhatta made a table of sines in the fifth century. The work also includes the rules for making up other Trigonometry tables of sines and sine differences. It is remarkable that his entire work follows the rules of Ganitha Sastra, or Mathematics, as well as those of Sanskrit Grammar.
Trigonometry linked Geometry to practical ends
The simplest example of this is the Pythagorean theorem. Using the straightforward concept of a right-angled triangle, the distance between two opposite ends of the hypotenuse could be computed easily. More complex trigonometric ratios such as the tangent, cotangent, and secant could also be calculated and unknown angles can be determined. Because it links the practical side of things to the more arcane concepts of Geometry, Trigonometry is considered an offshoot of Geometry.
How to picture trigonometric formulae
Although trigonometric functions appear complex, irrational, and tough to visualize, students will make a lot of progress by considering them as triangles within circles and triangles within spheres. These are namely visualized as planar or spherical figures. This is exactly how the Greek astronomer, Hipparchus of Nicaea, visualized the functions to arrive at the basics of trigonometry ratios.
Trigonometry got mankind massive answers
Before the advent of computers or even calculators, trigonometric formulae simplified the calculation of large distances and massive structures.
Trigonometry helped with navigation
Circa the 1700s, exploration of the heavens and the earth was in its nascent stages compared to now. For instance, the sundial was the one method of telling time with any accuracy when there was no clock present. At such a time, Trigonometry tables allowed navigators to create maps, read maps with a realistic sense of the distance between two points, and keep time. Navigators used compasses, clocks, and trigonometry tables to compute distances.
Trigonometry helped with the study of the earth
Given that trigonometric functions could be extrapolated for long distances using angles, ancient Egyptians used the angle of the Sun from different points on earth to compute the radius of the earth. This was an early application of trigonometry.
Trigonometry gave rise to the invention of the clinometer
The clinometer, a type of which is the inclinometer, is an instrument used to measure the angle of elevation. It helps in determining the height of objects and structures that cannot be measured manually. While a compass shows the direction in relation to the geographical north and south poles, the clinometer points the angle of elevation or slope along the y axis, against gravity. Through the angle found by the clinometer, the height of a tall structure can be determined using trigonometric principles.
Trigonometry truly enhanced the pace at which Mathematics, particularly Geometry, took a leap forward to practical usefulness.