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

```

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