This one wired trick

This commit is contained in:
alexander
2025-11-10 23:35:28 +01:00
parent 5b1c954574
commit 23d4bda871
10 changed files with 3900 additions and 6 deletions

54
src/Analysis1.typ Normal file
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#import "@preview/biceps:0.0.1": *
#import "@preview/cetz:0.4.2"
#import "lib/styles.typ": *
#import "lib/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),
[$tan(x)=sin(x)/cos(x)$],
[$cot(x)=cos(x)/sin(x)$],
[$tan(x)=-cot(x + pi/2)$],
[$cot(x)=-tan(x + pi/2)$],
[$cos(x - pi/2) = sin(x)$],
[$sin(x + pi/2) = cos(x)$],
)
$sin(x)cos(y) = 1/2sin(x - y) + 1/2sin(x + y)$
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
)