[VA] SRC#004- Fun with Sexagesimal Trigs

[Valentin Albillo]

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Hi, all:

Welcome to my brand new SRC#004, this time commemorating that this is my 300^th post here so if I'm not mistaken I'll be granted the description "Senior Member" from now on. What a treat !

Tired of trigs in radians ? Wanna see some trigs in sexagesimal degrees ? Read on !

Details:

If you're in the mood for a nice helping of awesome "sexagesimal" results go and try your hand at accurately evaluating the following trig expressions, either manually or else by writing a short bit of RPN/RPL/71BASIC/HPPL code for your preferred HP calculator (not Excel, Matlab, Mathematica, Python, Java, Haskell, C/C++, Wolfram Alpha, etc., there are many other forums/threads for that), namely:

\[ A = (\sqrt{3}\;+\;tan\;1º)\;(\sqrt{3}\;+\;tan\;2º)\;...\;(\sqrt{3}\;+\;tan\;29º) \]
\[ B = \frac{1}{sin\;45º \; sin\;46º} +\frac{1}{sin\;47º \; sin\;48º} \; + \;...\; + \; \frac{1}{sin\;133º \; sin\;134º} \]
\[ C = \left(1 - \frac{cos\;61º}{cos\;1º}\right) \; \left(1 - \frac{cos\;62º}{cos\;2º}\right) \; ... \; \left(1 - \frac{cos\;119º}{cos\;59º}\right) \]
\[ D = \left(1-\frac{1}{tan\;1º}\right)\;\left(1-\frac{1}{tan\;2º}\right)\; ...\; \left(1-\frac{1}{tan\;44º}\right) \]
\[ E = \left(2\;cos\;2^2º-\frac{1}{cos\;2^2º}\right)\;\left(2\;cos\;2^3º-\frac{1}{cos\;2^3º}\right)\;...\;\left(2\;cos\;2^{25}º-\frac{1}{cos\;2^{25}º}\right) \]
Once you've succeeded in accurately evaluating them you should attempt to identify the results that aren't immediately obvious (i.e.: if you get something like 1.7320508.. you should identify it as \(\sqrt{3}\)), which will be useful to gauge the accuracy obtained by comparing what you got with the exact results, benchmark-like.

You must not use anything other than your intuition and the help of your trusty HP calculator for the identification (in particular give the Internet a miss) but those of you using HP calcs with CAS might want to check if your CAS will produce the exact results at once or if at least it will simplify them to something much .. well, simpler !

Let's see your code, results and comments (try not to spoil early the fun for others), I will post mine within a few days.

V.
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