Added sine table and cc0 mark

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) $
+$ 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
+  ])
+

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"
+    ]
+}