From a97ba371f257ffcb29467142d00c59c4fe7205df Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Thu, 23 Dec 2021 22:52:31 +0100
Subject: more trigo stuff

---
 buch/chapters/030-geometrie/trigo/1.m | 33 +++++++++++++++++++++++++++++++++
 buch/chapters/030-geometrie/trigo/3.m | 13 +++++++++++++
 2 files changed, 46 insertions(+)
 create mode 100644 buch/chapters/030-geometrie/trigo/1.m
 create mode 100644 buch/chapters/030-geometrie/trigo/3.m

(limited to 'buch/chapters/030-geometrie/trigo')

diff --git a/buch/chapters/030-geometrie/trigo/1.m b/buch/chapters/030-geometrie/trigo/1.m
new file mode 100644
index 0000000..3eea249
--- /dev/null
+++ b/buch/chapters/030-geometrie/trigo/1.m
@@ -0,0 +1,33 @@
+#
+# 1.m
+#
+#
+n = 10;
+format long;
+
+function retval = snewtonstep(x, s)
+	corr = (-4*x*x*x+3*x-s) / (-12*x*x + 3);
+	retval = x - corr;
+end
+
+function retval = cnewtonstep(x, c)
+	corr = (4*x*x*x-3*x-c) / (12*x*x - 3);
+	retval = x - corr;
+end
+
+s0 = pi / 180;
+
+s3 = sind(3)
+c3 = cosd(3)
+
+r = zeros(n+1,2)
+r(1,1) = pi / 180;
+r(1,2) = sqrt(1-r(1,1)^2);
+
+for i = (1:n)
+	r(i+1,1) = snewtonstep(r(i,1), s3);
+	r(i+1,2) = cnewtonstep(r(i,2), c3);
+endfor
+
+r
+
diff --git a/buch/chapters/030-geometrie/trigo/3.m b/buch/chapters/030-geometrie/trigo/3.m
new file mode 100644
index 0000000..a1f8ed1
--- /dev/null
+++ b/buch/chapters/030-geometrie/trigo/3.m
@@ -0,0 +1,13 @@
+format long
+
+s15 = sqrt((2-sqrt(3))/4)
+c15 = sqrt((2+sqrt(3))/4)
+
+s36 = sqrt((5-sqrt(5))/8)
+c36 = sqrt((3+sqrt(5))/8)
+
+s18 = sqrt(1/2-c36/2)
+c18 = sqrt(1/2+c36/2)
+
+s3 = s18 * c15 - c18 * s15
+c3 = c18 * c15 + s18 * s15
-- 
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