#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
)