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