From b79719066bcc0360e6a1abc3e5e90cc92d01cfed Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Fri, 24 Dec 2021 09:48:45 +0100
Subject: Trigotabelle

---
 buch/chapters/030-geometrie/trigo/3.bc          | 260 ++++++++++++++++++++++++
 buch/chapters/030-geometrie/trigonometrisch.tex |   3 +
 2 files changed, 263 insertions(+)
 create mode 100644 buch/chapters/030-geometrie/trigo/3.bc

diff --git a/buch/chapters/030-geometrie/trigo/3.bc b/buch/chapters/030-geometrie/trigo/3.bc
new file mode 100644
index 0000000..2ee9026
--- /dev/null
+++ b/buch/chapters/030-geometrie/trigo/3.bc
@@ -0,0 +1,260 @@
+#
+# 3.bc -- compute values of trigonometric functions to an arbitrary
+#         number of digits for all multiples of 1 degree using only 
+#         basic arithmetic operations and square roots
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+scale=67
+
+s00=0
+c00=1
+
+s45=sqrt(2)/2
+c45=s45
+
+s30=0.5
+c30=sqrt(3)/2
+
+s15=sqrt(0.5-0.5*c30)
+c15=sqrt(0.5+0.5*c30)
+
+s36=sqrt((5-sqrt(5))/8)
+c36=sqrt((3+sqrt(5))/8)
+
+s72=2*s36*c36
+c72=c36^2-s36^2
+
+s18=sqrt(0.5-0.5*c36)
+c18=sqrt(0.5+0.5*c36)
+
+s09=sqrt(0.5-0.5*c18)
+c09=sqrt(0.5+0.5*c18)
+
+s03=s18*c15-c18*s15
+c03=c18*c15+s18*s15
+
+s06=s15*c09-c15*s09
+c06=c15*c09+s15*s09
+
+s12=s30*c18-c30*s18
+c12=c30*c18+s30*s18
+
+s21=s30*c09-c30*s09
+c21=c30*c09+s30*s09
+
+s24=s15*c09+c15*s09
+c24=c15*c09-s15*s09
+
+s27=s45*c18-c45*s18
+c27=c45*c18+s45*s18
+
+s33=s45*c12-c45*s12
+c33=c45*c12+s45*s12
+
+s39=s30*c09+c30*s09
+c39=c30*c09-s30*s09
+
+s42=s30*c12+c30*s12
+c42=c30*c12-s30*s12
+
+s=3.1415926535/180
+c=sqrt(1-s*s)
+
+s=s-(4*s*s*s-3*s+s03)/(12*s*s-3)
+s=s-(4*s*s*s-3*s+s03)/(12*s*s-3)
+s=s-(4*s*s*s-3*s+s03)/(12*s*s-3)
+s=s-(4*s*s*s-3*s+s03)/(12*s*s-3)
+s=s-(4*s*s*s-3*s+s03)/(12*s*s-3)
+s=s-(4*s*s*s-3*s+s03)/(12*s*s-3)
+s01=s
+
+c=c-(4*c*c*c-3*c-c03)/(12*c*c-3)
+c=c-(4*c*c*c-3*c-c03)/(12*c*c-3)
+c=c-(4*c*c*c-3*c-c03)/(12*c*c-3)
+c=c-(4*c*c*c-3*c-c03)/(12*c*c-3)
+c=c-(4*c*c*c-3*c-c03)/(12*c*c-3)
+c=c-(4*c*c*c-3*c-c03)/(12*c*c-3)
+c01=c
+
+s02=s03*c01-c03*s01
+c02=c03*c01+s03*s01
+
+s04=s03*c01+c03*s01
+c04=c03*c01-s03*s01
+
+s05=s06*c01-c06*s01
+c05=c06*c01+s06*s01
+
+s07=s06*c01+c06*s01
+c07=c06*c01-s06*s01
+
+s08=s09*c01-c09*s01
+c08=c09*c01+s09*s01
+
+s10=s09*c01+c09*s01
+c10=c09*c01-s09*s01
+
+s11=s12*c01-c12*s01
+c11=c12*c01+s12*s01
+
+s13=s12*c01+c12*s01
+c13=c12*c01-s12*s01
+
+s14=s15*c01-c15*s01
+c14=c15*c01+s15*s01
+
+s16=s15*c01+c15*s01
+c16=c15*c01-s15*s01
+
+s17=s18*c01-c18*s01
+c17=c18*c01+s18*s01
+
+s19=s18*c01+c18*s01
+c19=c18*c01-s18*s01
+
+s20=s21*c01-c21*s01
+c20=c21*c01+s21*s01
+
+s22=s21*c01+c21*s01
+c22=c21*c01-s21*s01
+
+s23=s24*c01-c24*s01
+c23=c24*c01+s24*s01
+
+s25=s24*c01+c24*s01
+c25=c24*c01-s24*s01
+
+s26=s27*c01-c27*s01
+c26=c27*c01+s27*s01
+
+s28=s27*c01+c27*s01
+c28=c27*c01-s27*s01
+
+s29=s30*c01-c30*s01
+c29=c30*c01+s30*s01
+
+s31=s30*c01+c30*s01
+c31=c30*c01-s30*s01
+
+s32=s33*c01-c33*s01
+c32=c33*c01+s33*s01
+
+s34=s33*c01+c33*s01
+c34=c33*c01-s33*s01
+
+s35=s36*c01-c36*s01
+c35=c36*c01+s36*s01
+
+s37=s36*c01+c36*s01
+c37=c36*c01-s36*s01
+
+s38=s39*c01-c39*s01
+c38=c39*c01+s39*s01
+
+s40=s39*c01+c39*s01
+c40=c39*c01-s39*s01
+
+s41=s42*c01-c42*s01
+c41=c42*c01+s42*s01
+
+s43=s42*c01+c42*s01
+c43=c42*c01-s42*s01
+
+s44=s45*c01-c45*s01
+c44=c45*c01+s45*s01
+
+s00
+s01
+s02
+s03
+s04
+s05
+s06
+s07
+s08
+s09
+s10
+s11
+s12
+s13
+s14
+s15
+s16
+s17
+s18
+s19
+s20
+s21
+s22
+s23
+s24
+s25
+s26
+s27
+s28
+s29
+s30
+s31
+s32
+s33
+s34
+s35
+s36
+s37
+s38
+s39
+s40
+s41
+s42
+s43
+s44
+s45
+
+c00
+c01
+c02
+c03
+c04
+c05
+c06
+c07
+c08
+c09
+c10
+c11
+c12
+c13
+c14
+c15
+c16
+c17
+c18
+c19
+c20
+c21
+c22
+c23
+c24
+c25
+c26
+c27
+c28
+c29
+c30
+c31
+c32
+c33
+c34
+c35
+c36
+c37
+c38
+c39
+c40
+c41
+c42
+c43
+c44
+c45
+
diff --git a/buch/chapters/030-geometrie/trigonometrisch.tex b/buch/chapters/030-geometrie/trigonometrisch.tex
index be51e89..51a8254 100644
--- a/buch/chapters/030-geometrie/trigonometrisch.tex
+++ b/buch/chapters/030-geometrie/trigonometrisch.tex
@@ -732,6 +732,9 @@ Mit einer einzigen Anwendung des Additionstheorems kann man jetzt
 aus den Werten der Tabelle~\ref{buch:geometrie:trigo:tabelle}
 die Werte von Sinus und Kosinus für jedes ganzzahlige
 Vielfache von $1^\circ$ berechnen.
+Das Skript \texttt{3.bc} im Repository führt dies durch und demonstriert,
+dass für die Berechnung aller Werte nur die arithmetischen Operationen
+und Quadratwurzeln nötig sind.
 \begin{table}
 \centering
 \begin{tabular}{|>{$}c<{$}|>{$}r<{$}|>{$}r<{$}|}
-- 
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