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Empfehlung 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

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
tangent, left parenthesis, theta, plus, \phi, right parenthesis, equals, start fraction, tangent, theta, plus, tangent, \phi, divided by, 1, minus, tangent, theta, tangent, \phi, end fraction
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
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
tanθ2=±1cosθ1+cosθ=       1cosθsinθ=       sinθ1+cosθ\begin{aligned} \tan\dfrac{\theta}{2}&=\pm\sqrt{\dfrac{1-\cos\theta}{1+\cos\theta}}\\ \\ &=~~~~~~~\dfrac{1-\cos\theta}{\sin\theta}\\ \\ &=~~~~~~~\dfrac{\sin\theta}{1+\cos\theta}\end{aligned}

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

Kofunktionsidentitäten

sine, theta, equals, cosine, left parenthesis, start fraction, pi, divided by, 2, end fraction, minus, theta, right parenthesis
cosine, theta, equals, sine, left parenthesis, start fraction, pi, divided by, 2, end fraction, minus, theta, right parenthesis
tangent, theta, equals, cotangent, left parenthesis, start fraction, pi, divided by, 2, end fraction, minus, theta, right parenthesis
cotangent, theta, equals, tangent, left parenthesis, start fraction, pi, divided by, 2, end fraction, minus, theta, right parenthesis
\sec, theta, equals, \csc, left parenthesis, start fraction, pi, divided by, 2, end fraction, minus, theta, right parenthesis
\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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