Genetic Code For Sine

摘要

The computation of the approximate values of the trigonometric sines was discovered by Bhaskara I (c. 600-c.680), a seventh century Indian mathematician and is known as the Bjaskara’s I’s sine approximation formula. The formula is given in his treatise titled Mahabhaskariya. In the 14th century, Madhava of Sangamagrama, a Kerala mathematician astronomer constructed the table of trigonometric sines of various angles. Madhava’s table gives the measure of angles in arcminutes, arcseconds and sixtieths of an arcsecond. The search for more accurate formulas led to the discovery of the power series expansion by Madhava of Sangamagrama (c.1350-c. 1425), the founder of the Kerala school of astronomy and mathematics. In 1715, the Taylor series was introduced by Brook Taylor an English mathematician. If the Taylor series is centered at zero, it is called a Maclaurin series, named after the Scottish mathematician Colin Maclaurin. Some of the important Maclaurin series expansions include trigonometric functions. This paper introduces the genetic code of the sine of an angle without using power series expansion. The genetic code using square root approach reveals the pattern in the signs (plus, minus) and sequence of numbers in the sine of an angle. The square root approach complements the Pythagoras method, provides a better understanding of calculating an angle and will be useful for teaching the concepts of angles in trigonometry.