Exact Values for Sine and Cosine
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
This Demonstration finds the exact values for sine and cosine at angles whose degree measure is a multiple of 3.
Contributed by: Christopher Moretti (October 2007)
Open content licensed under CC BY-NC-SA
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, for example).