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Trigonometrie
Kurs: Trigonometrie > Lerneinheit 4
Lektion 5: Trigonometrische Identitäten verwendenEmpfehlung zu Trigonometrischer Identität
Schaue nach UND verstehe alle deine bevorzugten trigonometrischen Identitäten
Reziproke und Quotientidentitäten
\sec, left parenthesis, theta, right parenthesis, equals, start fraction, 1, divided by, cosine, left parenthesis, theta, right parenthesis, end fraction
\csc, left parenthesis, theta, right parenthesis, equals, start fraction, 1, divided by, sine, left parenthesis, theta, right parenthesis, end fraction
cotangent, left parenthesis, theta, right parenthesis, equals, start fraction, 1, divided by, tangent, left parenthesis, theta, right parenthesis, end fraction
tangent, left parenthesis, theta, right parenthesis, equals, start fraction, sine, left parenthesis, theta, right parenthesis, divided by, cosine, left parenthesis, theta, right parenthesis, end fraction
cotangent, left parenthesis, theta, right parenthesis, equals, start fraction, cosine, left parenthesis, theta, right parenthesis, divided by, sine, left parenthesis, theta, right parenthesis, end fraction
\csc, left parenthesis, theta, right parenthesis, equals, start fraction, 1, divided by, sine, left parenthesis, theta, right parenthesis, end fraction
cotangent, left parenthesis, theta, right parenthesis, equals, start fraction, 1, divided by, tangent, left parenthesis, theta, right parenthesis, end fraction
tangent, left parenthesis, theta, right parenthesis, equals, start fraction, sine, left parenthesis, theta, right parenthesis, divided by, cosine, left parenthesis, theta, right parenthesis, end fraction
cotangent, left parenthesis, theta, right parenthesis, equals, start fraction, cosine, left parenthesis, theta, right parenthesis, divided by, sine, left parenthesis, theta, right parenthesis, end fraction
Trigonometrischer Pythagoras
sine, squared, left parenthesis, theta, right parenthesis, plus, cosine, squared, left parenthesis, theta, right parenthesis, equals, 1, squared
tangent, squared, left parenthesis, theta, right parenthesis, plus, 1, squared, equals, \sec, squared, left parenthesis, theta, right parenthesis
cotangent, squared, left parenthesis, theta, right parenthesis, plus, 1, squared, equals, \csc, squared, left parenthesis, theta, right parenthesis
Identitäten, die aus Summen, Differenzen, Vielfachen und Bruchteilen von Winkeln stammen
Diese sind alle eng verwandt, aber schauen wir uns jede Art an.
Winkelsummen- und Differenzidentitäten
sine, left parenthesis, theta, plus, \phi, right parenthesis, equals, sine, theta, cosine, \phi, plus, cosine, theta, sine, \phi
sine, left parenthesis, theta, minus, \phi, right parenthesis, equals, sine, theta, cosine, \phi, minus, cosine, theta, sine, \phi
cosine, left parenthesis, theta, plus, \phi, right parenthesis, equals, cosine, theta, cosine, \phi, minus, sine, theta, sine, \phi
cosine, left parenthesis, theta, minus, \phi, right parenthesis, equals, cosine, theta, cosine, \phi, plus, sine, theta, sine, \phi
sine, left parenthesis, theta, minus, \phi, right parenthesis, equals, sine, theta, cosine, \phi, minus, cosine, theta, sine, \phi
cosine, left parenthesis, theta, plus, \phi, right parenthesis, equals, cosine, theta, cosine, \phi, minus, sine, theta, sine, \phi
cosine, left parenthesis, theta, minus, \phi, right parenthesis, equals, cosine, theta, cosine, \phi, plus, sine, theta, sine, \phi
tangent, left parenthesis, theta, minus, \phi, right parenthesis, equals, start fraction, tangent, theta, minus, tangent, \phi, divided by, 1, plus, tangent, theta, tangent, \phi, end fraction
Doppelwinkelidentitäten
sine, left parenthesis, 2, theta, right parenthesis, equals, 2, sine, theta, cosine, theta
cosine, left parenthesis, 2, theta, right parenthesis, equals, 2, cosine, squared, theta, minus, 1
tangent, left parenthesis, 2, theta, right parenthesis, equals, start fraction, 2, tangent, theta, divided by, 1, minus, tangent, squared, theta, end fraction
cosine, left parenthesis, 2, theta, right parenthesis, equals, 2, cosine, squared, theta, minus, 1
tangent, left parenthesis, 2, theta, right parenthesis, equals, start fraction, 2, tangent, theta, divided by, 1, minus, tangent, squared, theta, end fraction
Halbwinkelidentitäten
sine, start fraction, theta, divided by, 2, end fraction, equals, plus minus, square root of, start fraction, 1, minus, cosine, theta, divided by, 2, end fraction, end square root
cosine, start fraction, theta, divided by, 2, end fraction, equals, plus minus, square root of, start fraction, 1, plus, cosine, theta, divided by, 2, end fraction, end square root
sine, start fraction, theta, divided by, 2, end fraction, equals, plus minus, square root of, start fraction, 1, minus, cosine, theta, divided by, 2, end fraction, end square root
cosine, start fraction, theta, divided by, 2, end fraction, equals, plus minus, square root of, start fraction, 1, plus, cosine, theta, divided by, 2, end fraction, end square root
Symmetrie- und Periodizitätsidentitäten
sine, left parenthesis, minus, theta, right parenthesis, equals, minus, sine, left parenthesis, theta, right parenthesis
cosine, left parenthesis, minus, theta, right parenthesis, equals, plus, cosine, left parenthesis, theta, right parenthesis
tangent, left parenthesis, minus, theta, right parenthesis, equals, minus, tangent, left parenthesis, theta, right parenthesis
sine, left parenthesis, theta, plus, 2, pi, right parenthesis, equals, sine, left parenthesis, theta, right parenthesis
cosine, left parenthesis, theta, plus, 2, pi, right parenthesis, equals, cosine, left parenthesis, theta, right parenthesis
tangent, left parenthesis, theta, plus, pi, right parenthesis, equals, tangent, left parenthesis, theta, right parenthesis
cosine, left parenthesis, minus, theta, right parenthesis, equals, plus, cosine, left parenthesis, theta, right parenthesis
tangent, left parenthesis, minus, theta, right parenthesis, equals, minus, tangent, left parenthesis, theta, right parenthesis
sine, left parenthesis, theta, plus, 2, pi, right parenthesis, equals, sine, left parenthesis, theta, right parenthesis
cosine, left parenthesis, theta, plus, 2, pi, right parenthesis, equals, cosine, left parenthesis, theta, right parenthesis
tangent, left parenthesis, theta, plus, pi, right parenthesis, equals, tangent, left parenthesis, theta, right parenthesis
Kofunktionsidentitäten
\csc, theta, equals, \sec, left parenthesis, start fraction, pi, divided by, 2, end fraction, minus, theta, right parenthesis
Anhang: Alle trigonometrischen Verhältnisse im Einheitskreis
Verwende den beweglichen Punkt, um zu sehen, wie sich die Längen der Verhältnisse entsprechend dem Winkel ändern.
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