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Trigonometrinės formulės

  • {statinis prieš ∠ A}/{įžambinė}=sin ∠ A
  • {statinis prie ∠ A}/{įžambinė}=cos ∠ A
  • {statinis prieš ∠ A}/{statinis prie ∠ A}=tg ∠ A
  • {statinis prie ∠ A}/{statinis prieš ∠ A}=ctg ∠ A
30° 45° 60°
sin alpha 1/2 sqrt{2}/2 sqrt{3}/2
cos alpha sqrt{3}/2 sqrt{2}/2 1/2
tg alpha sqrt{3}/3 1 sqrt{3}
ctg alpha sqrt{3} 1 sqrt{3}/3
  • sin^2 alpha + cos^2 alpha=1
  • tg alpha={sin alpha}/{cos alpha}
  • tg alpha * ctg alpha = 1
  • sin 2alpha = 2 * sin alpha * cos alpha
  • cos 2alpha = cos^2 alpha - sin^2 alpha = 1 - 2sin^2 alpha = 2cos^2 alpha - 1
  • 1 + tg^2 alpha = 1/{cos^2 alpha}, 1 + ctg^2 alpha = 1/{sin^2 alpha}
  • 2 * sin^2 alpha = 1 - cos 2*alpha, 2 * cos^2 alpha = 1 + cos^2 alpha
  • sin(alpha pm beta) = sin alpha * cos beta pm cos alpha * sin beta
  • cos(alpha pm beta) = cos alpha * cos beta overline{+} sin alpha * sin beta
  • sin alpha pm sin beta = 2 * sin {{alpha pm beta}/2} * cos {{alpha overline{+} beta}/2}
  • cos alpha + cos beta = 2*cos {{alpha + beta}/2} * cos {{alpha - beta}/2}
  • cos alpha - cos beta = -2 * sin {{alpha + beta}/2} * sin {{alpha - beta}/2}
  • tg (alpha pm beta) = {tg alpha pm tg beta}/{1 overline{+} tg alpha * tg beta}

Sinusų teorema ir jos išvada

a/{sin alpha} = b/{sin beta} = c/{sin gamma} = 2R

R - spindulys

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