From 95f83c8291a60324283c343ba1f0d5f765ee8c1c Mon Sep 17 00:00:00 2001
From: alexander <alexander@xstation>
Date: Sun, 18 Jan 2026 13:47:15 +0100
Subject: [PATCH] Added sine table and cc0 mark

---
 src/Analysis_rewrite.typ |  61 ++++++++++++++++++++++++++++++++++-----
 src/images/cc0.png       | Bin 0 -> 980 bytes
 src/sintable.json        |  18 ++++++++++++
 3 files changed, 72 insertions(+), 7 deletions(-)
 create mode 100644 src/images/cc0.png
 create mode 100644 src/sintable.json

diff --git a/src/Analysis_rewrite.typ b/src/Analysis_rewrite.typ
index a8443c8..48bd798 100644
--- a/src/Analysis_rewrite.typ
+++ b/src/Analysis_rewrite.typ
@@ -1,4 +1,5 @@
 #import "lib/common_rewrite.typ" : *
+#import "@preview/mannot:0.3.1"
 
 #set page(
   paper: "a4", 
@@ -9,12 +10,15 @@
     right: 5mm
   ),
   flipped:true,
-  numbering: "— 1 —",
-  number-align: center
-)
-
-#set text(
-  size: 8pt,
+  footer: context [
+    #grid(
+      align: center,
+      columns: (1fr, 1fr, 1fr),
+      [#align(left, datetime.today().display("[day].[month].[year]"))], 
+      [#align(center, counter(page).display("- 1 -"))], 
+      [#align(right, image("images/cc0.png", height: 5mm,))]
+    )
+  ],
 )
 
 #place(top+center, scope: "parent", float: true, heading(
@@ -110,9 +114,13 @@
       [$ cos(x) = (e^(i x) + e^(-i x))/(2) $]
     )
     #subHeading(fill: colorAllgemein)[Trigonmetrie]
+    *Additionstheorem* \
     $sin(x+y) = cos(x)sin(y) + sin(x)cos(y)$ \
     $cos(x+y) = cos(x)cos(y) - sin(x)sin(y)$ \
+    $tan(x) + tan(y) = (tan(a) + tan(b))/(1 - tan(a) tan(b))$ \
+    $arctan(x) + arctan(y) = arctan((x+y)/(1 - x y))$ \
 
+    *Doppelwinkel Formel* \
     $cos(2x) = cos^2(x) - sin^2(x)$ \
     $sin(2x) = 2sin(x)cos(x)$
 
@@ -470,6 +478,25 @@
   #colbreak()
 ]
 
+#bgBlock(fill: colorAllgemein, [
+  #subHeading(fill: colorAllgemein, [Sin-Table])
+
+  #let data = json("sintable.json")
+  #table(
+    columns: data.at("x").len() + 1,
+    rows: data.keys().len(),
+    stroke: none,
+    table.hline(stroke: (thickness: 0.3mm)),
+    fill: (x, y) => if (calc.rem(y, 2) == 0) { color.lighten(colorAllgemein, 10%) } else { white },
+      ..for (label) in data.keys() {
+      ([*#eval(label, mode: "math")*], table.hline(stroke: (thickness: 0.3mm)), )
+      for i in data.at(label) {
+        (eval(i, mode: "math"),)
+      }
+    }
+  )
+])
+
 #pagebreak()
 
 == Folgen in $CC$
@@ -516,4 +543,24 @@ Konvergenz Radius $R = [0, infinity)$$$
   z in CC &abs(z - z_0) > R &: "Divergent"
 )$
 
-$ R = limsup_(n -> infinity) $
\ No newline at end of file
+$ R = limsup_(n -> infinity) $
+  #bgBlock(fill: colorIntegral, [
+    #subHeading(fill: colorIntegral, [Integral])
+
+    Summen: $integral f(x) + g(x) d x = integral f(x) d x + integral g(x)$
+
+    Vorfaktoren: $integral lambda f(x) d x = lambda f(x) d x$
+
+    *Partial Integration*
+    
+    $integral u(x) dot v'(x) d x = u(x)v(x) - integral u'(x) dot v(x)$
+
+    *Subsitution*
+
+    $integral_(x_0)^(x_1) f\(underbrace(g(x), "t")\) dot g'(x) d x$
+    
+    1. Ersetzung: $ d x := d t dot 1/(g'(x))$ und $t := g(x)$
+    2. Grenzen: $t_0 = g(x_0)$, $t_1 = g(x_1)$
+    3. $x$-kürzen sich weg
+  ])
+
diff --git a/src/images/cc0.png b/src/images/cc0.png
new file mode 100644
index 0000000000000000000000000000000000000000..1098629811b136a68d1519505a28aa14c0ef8654
GIT binary patch
literal 980
zcmV;_11tQAP)<h;3K|Lk000e1NJLTq003A30018d0{{R3R2KTu0002+P)t-s00030
z|NsC0|Nj2|{r&y>`}_L&_xbtx`S|wu`1tqt_xASo_Vx4i_4V}h^z-xc^78WW@$v8P
z@9gaC>gww4>f!3@=j!R_>FDU_=jG?;=jP_-<>lq%<mBSw;^E=p-{0Tf-rn8a-PzgM
z*4Eb5)z#C})6&w?&(F`!&d$xv&CAQn%F4>c#l^qBzrMb{y1Kfzx3{maub-cvo}QkU
zmzR)`kdKd#j*gCvjg5<oi;9YhgoK2De}8&<dT(!UZEbC3Wo2JqUsF?4Pft%xO-(^T
zK|en~K0ZD%F)=SMFDxu9A0HnX85s``4+;wj8jOH`00002bW%=J{{ZE;FiHRb0+C5X
zK~#9!wblu5)G!c+;g4xcp&X@Vxm)m34pU%&7;u4_KnM&qCj9?@gB^EMRcb1<?7q^j
zlsz6f(d586ETzQWSV{nBDV>Bhr_`chT}SjquU6OZ|HA)9C6D8}{Y#T+yAW6f0IfAd
z#tMM%4|bl01;E)2hK}OAwKaYH2RZTHH;6vwS4<mqMB|b20yNgj8E^wMlrqejS1s^m
z^5g(HPpruc3DQf*7-BFXMIMf{qIMLnfHr%Al;p7pz?+@DP+&mu01J#7;7E*)-6$N<
z6|GP5h;;b5HT_&*Z^;gD$_}tljnRk<VEf+#b;h|2$?oK3fthVLz_nBqj$sE_HwM>0
zUT~Wc$$DNgu)jGy%y5qc;w)yEGwi)jFtloGvSV;wOR57j11MVo&BpfE8C>?sm9HF_
zQW*}K$aG_HfS;X(0RjX{wUG6@2_EX?R3HRk48{Ok#NJQ&0?*ya6-QJI$cYs<%<Ma$
zWv&7OGf=YwVtxzU1oj9V&OFB1<l|#pU{7qwKu9~Kq7XGO#DL5HkUSX_gyih0fTpHQ
zg#z|Bwr5jOQK%Br_DmHi!&*~)1e+1q0B$zN$%QF%{BU!M0w+<J0c6IIC&Or|(WbzT
zDw2Oc^JM+{!3=f@p6z%|R58PnQ55qh`MVLAi>3srR+X#WtBdyzhf`XkA>(^VG&Rg!
z+H~X!9MuR+P4UPuYbtKNw)GCVq_B;E*JN4*4mEeq2@6o!ekuZL4&&G3$aGW{6SsQh
z@$W_4K?Fc>tQ5P5<gTnwek|yo*I}ruR@Sb4!(w1kKB6x;MXMXTZ{L6XG<P2gJlMl?
z#p>1VM|;m-%-u5pYv)ht!ew>y_MQ2=g{3{aEv>)J=c!SwH-csW0000<MNUMnLSTY-
CZ}r*$

literal 0
HcmV?d00001

diff --git a/src/sintable.json b/src/sintable.json
new file mode 100644
index 0000000..22f880c
--- /dev/null
+++ b/src/sintable.json
@@ -0,0 +1,18 @@
+
+{
+    "x": [
+        "0", "pi/6", "pi/4", "pi/3", "pi/2", "(2pi)/3", "(3pi)/4", "(5pi)/6", "pi", "(7pi)/6", "(5pi)/4", "(4pi)/3", "(3pi)/2", "(5pi)/3", "(7pi)/4", "(11pi)/6", "2pi"
+    ],
+    "alpha": [
+        "0°", "30°", "45°", "60°", "90°", "120°", "135°", "150°", "180°", "210°", "225°", "240°", "270°", "300°", "315°", "330°", "360°"
+    ],
+    "cos(x)": [
+        "1", "sqrt(3)/2", "sqrt(2)/2", "1/2", "0", "-1/2", "-sqrt(2)/2", "-sqrt(3)/2", "-1", "-sqrt(3)/2", "-sqrt(2)/2", "-1/2", "0", "1/2", "sqrt(2)/2", "sqrt(3)/2", "1"
+    ],
+    "sin(x)": [
+        "0", "1/2", "sqrt(2)/2", "sqrt(3)/2", "1", "sqrt(3)/2", "sqrt(2)/2", "1/2", "0", "-1/2", "-sqrt(2)/2", "-sqrt(3)/2", "-1", "-sqrt(3)/2", "-sqrt(2)/2", "-1/2", "0"
+    ],
+    "tan(x)": [
+        "0", "1/sqrt(3)", "1", "sqrt(3)", "x", "-sqrt(3)", "-1", "-1/sqrt(3)", "0", "1/sqrt(3)", "1", "sqrt(3)", "x", "-sqrt(3)", "-1", "-1/sqrt(3)", "0"
+    ]
+}
\ No newline at end of file