The predecessor of the modern trigonometric function known as the sine of an angle was born, apparently, in India. The Greek trigonometry had been based on the functional relationship between the chords of a circle and the central angles they subtend. The Indians, on the other hand, used half of a chord of a circle as their basic trigonometric function. The Indian (or Hindu) Sine (usually written with a capital letter to distinguish it from the modern Sine) of an arc in a circle is defined as half the length of the chord of double the arc. Thus the (Indian) Sine of an arc \(\alpha \) is equal to R \(\sin \theta \) where R is the radius of the circle of reference and \(\sin \theta \) is the modern sine of the angle \(\theta \) subtended at the centre by the arc \(\alpha \).