2.9 Historical Notes

The study of trigonometry was first started in India. The ancient Indian Mathematicians, Aryabhata (476 AD), Brahmagupta (598 AD), Bhaaskar 1 (600 AD) and Bhaaskar 2 (1114 AD) got important results of trigonometry. All this knowledge went from India to Arabia and then from there to Europe. The Greeks had also started the study of trigonometry but their approach was so clumsy that when the Indian approach became known, it was immediately adopted throughout the world.

In India, the predecessor of the modern trigonometric functions, known as the sine of an angle, and the introduction of the sine function represents one of the main contribution of the siddhantas (Sanskrit astronomical works) to mathematics.

Bhaaskar 1 (about 600 AD) gave formulae to find the values of sine functions for angles more than 90°. A sixteenth century Malayalam work Yuktibhasa contains a proof for the expansion of sin (A + B). Exact expression for sines or cosines of 18°, 36°, 54°, 72°, etc, were given by Bhaaskar II.

The symbols sin^−1 (x), cos^−1 (x), etc, for arc sin x, arc cos x, etc, were suggested by the astronomer Sir John F.W. Hersehel (1813) The name of Thales (about 600 B.C.) is invariably associated with height and distance problems. He is credited with the determination of the height of a great pyramid in Egypt by measuring shadows of the pyramid and an auxiliary staff (or gnomon) of known height, and comparing the ratios:

H/S = h/s = tan (sun’s altitude)

Thales is also said to have calculated the distance of a ship at sea through the proportionality of sides of similar triangles. Problems on height and distance using the similarity property are also found in ancient Indian works.

Congratulations! You have completed this chapter. I hope you enjoyed studying this chapter. In case you found any difficulties in this chapter or have any suggestions to improve it, please write to us at ‘blind2Visionary@gmail.com’.

End of Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions for Blind and Visually Impaired Students by Dr T K Bansal.