Stupid Mma Tricks

*To*: mathgroup at yoda.physics.unc.edu*Subject*: Stupid Mma Tricks*From*: Richard Mercer <richard at rmercer.wright.edu>*Date*: Wed, 09 Mar 1994 08:54:37 -0500

One of my students yesterday used Mathematica to evaluate sin(pi/12), and guess what came out! In[1]:= Sin[Pi/12] Out[1]= -1 + Sqrt[3] ------------ 2 Sqrt[2] You also get exact answer for other multiples of pi/12 and other trig functions. However sin(pi/8), sin(pi/24), etc. received no such special attention -- they remain unevaluated. Apparently somebody thinks Pi/12 ( = 15 degrees) is special. Then it struck me. What if all exact trig values are calculated through some kinky algorithm that deals strictly with multiples of pi/12, so that e.g. when you find sin(pi/3), it is handled as sin(4 pi/12)? Perhaps Mathematica calculates the fourth power of the 2x2 rotation matrix for an angle of pi/12, then extracts the values of sin(pi/3) and cos(pi/3) from that matrix? Would somebody please confirm or deny this ugly rumor? Richard Mercer