Added sin-table

This commit is contained in:
alexander
2025-11-09 12:18:39 +01:00
parent 6be441b3a1
commit 5b1c954574
4 changed files with 133 additions and 36 deletions

53
Analysis1.typ Normal file
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@@ -0,0 +1,53 @@
#import "@preview/biceps:0.0.1": *
#import "@preview/cetz:0.4.2"
#import "styles.typ": *
#import "common.typ": *
#show: stdTemplate
#flexwrap( // Trigonometric formulas
main-spacing: 1mm,
cross-spacing: 1mm,
stdBlock([
$sin(x+y) = cos(x)sin(y) + sin(x)cos(y)$ \
$cos(x+y) = cos(x)cos(y) - sin(x)sin(y)$ \
$cos(2x) = cos^2(x) - sin^2(x)$ \
$sin(2x) = 2sin(x)cos(x)$
#grid(
gutter: 5mm,
columns: (auto, auto),
[$cos^2(x) = (1 + cos(2x))/2$],
[$sin^2(x) = (1 - cos(2x))/2$]
)
$cos^2(x) + sin^2(x) = 1$
#grid(
gutter: 5mm,
columns: (auto, auto),
[$cos(-x) = cos(x)$],
[$sin(-x) = -sin(x)$],
)
Subsitution mit Hilfsvariable
#grid(
gutter: 5mm,
row-gutter: 3mm,
columns: (auto, auto),
[$tan(x)=sin(x)/cos(x)$],
[$cot(x)=cos(x)/sin(x)$],
[$tan(x)=-cot(x + pi/2)$],
[$cot(x)=-tan(x + pi/2)$],
[$cos(x - pi/2) = sin(x)$],
[$sin(x + pi/2) = cos(x)$],
)
Für $x in [-1, 1]$ \
$arcsin(x) = -arccos(x) - pi/2 in [-pi/2, pi/2]$ \
$arccos(x) = -arcsin(x) + pi/2 in [0, pi]$
]),
sinTable
)

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@@ -1,21 +1,12 @@
#import "@preview/biceps:0.0.1" : * #import "@preview/biceps:0.0.1" : *
#import "styles.typ" : *
#set text( #show: stdTemplate
size: 8pt
)
#set page(
margin: 5mm
)
#flexwrap( #flexwrap(
main-spacing: 1mm, main-spacing: 1mm,
cross-spacing: 1mm, cross-spacing: 1mm,
block( stdBlock([
stroke: 0.2mm,
spacing: 1mm,
inset: 2mm,
[
*Halbgruppe:* $(M, compose): M times M arrow M$ *Halbgruppe:* $(M, compose): M times M arrow M$
- Assoziativgesetz: $a dot (b dot c) = (a dot b) dot c$ - Assoziativgesetz: $a dot (b dot c) = (a dot b) dot c$
*Monoid* Halbgruppe $M$ mit: *Monoid* Halbgruppe $M$ mit:
@@ -33,15 +24,11 @@
- Kommutativ Gruppe unter $(M, +)$ - Kommutativ Gruppe unter $(M, +)$
- Kommutativ Gruppe unter $(M, times)$ - Kommutativ Gruppe unter $(M, times)$
- Distributiv Gesetz: $(a + b) dot c = (a dot c) + (a dot b)$ - Distributiv Gesetz: $(a + b) dot c = (a dot c) + (a dot b)$
]),
stdBlock(
[
asd
] ]
), ),
block(
stroke: 0.2mm,
spacing: 1mm,
inset: 2mm,
[
]
)
) )

22
common.typ Normal file
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#import "styles.typ": *
#let sinTable = [
#table(
inset: 1.5mm,
stroke: (thickness: 0.2mm),
columns: 4,
table.header(
[x], [deg], [cos(x)], [sin(x)]
),
[$0$], [$0°$], hlMath([$1$], color: hlGreen), hlMath([$0$]),
[$pi/6$], [$30°$], hlMath([$sqrt(3)/2$], color: hlGreen), hlMath([$1/2$], color: hlGreen),
[$pi/4$], [$45°$], hlMath([$sqrt(2)/2$], color: hlGreen), hlMath([$sqrt(2)/2$], color: hlGreen),
[$pi/3$], [$60°$], hlMath([$1/2$], color: hlGreen), hlMath([$sqrt(3)/2$], color: hlGreen),
[$pi/2$], [$90°$], hlMath([$0$]), hlMath([$1$], color: hlGreen),
[$2/3pi$], [$120°$], hlMath([$-1/2$], color: hlRed), hlMath([$sqrt(3)/2$], color: hlGreen),
[$3/4pi$], [$135°$], hlMath([$-sqrt(2)/2$], color: hlRed), hlMath([$sqrt(2)/2$], color: hlGreen),
[$5/6pi$], [$150°$], hlMath([$-sqrt(3)/2$], color: hlRed), hlMath([$1/2$], color: hlGreen),
[$pi$], [$180°$], hlMath([$-1$], color: hlRed), hlMath([$0$]),
[$3/2pi$], [$270°$], hlMath([$0$]), hlMath([$-1$], color: hlRed)
)
]

35
styles.typ Normal file
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#let stdTemplate(doc) = [
#set text(
size: 8pt
)
#set page(
margin: 5mm
)
#doc
]
#let hlMath(content, color: rgb("#fffe69")) = box(
content,
outset: 2pt,
fill: color,
)
#let hlRed = rgb("#ff6969");
#let hlGreen = rgb("#76ff69");
#let stdBlock(content) = {
block(
stroke: 0.2mm,
spacing: 1mm,
inset: 2mm,
content
)
}
/* Usage examples:
#blockm("Hello", top: 10pt, bottom: 10pt)
#blockm(#p("Paragraph inside a margin-set block."), left: 12pt, right: 12pt)
*/