Exact Values for Sine and Cosine

The underlying functions newsine and newcosine work by breaking a given angle down into multiples of 90, 30, 15, 3, and 1 degree(s). The values at 3 degrees were found using combinations of 15 and 72 degrees, and the values at 1 degree by using the sine and cosine triple angle formulas and solving the resultant cubics. The Demonstration slider is restricted to angles whose degree measure is a multiple of 3, as other angles result in complicated expressions using complex numbers that cannot fit in a standard size Demonstration window without being illegible. These values can still be accessed using the underlying functions newsine and newcosine (newsine[73], for example).