Sinusrelationen
\( \frac{\sin \left( A \right)}{a} = \frac{\sin \left( B \right)}{b} = \frac{\sin \left( C \right)}{c} = \frac{1}{2 \cdot R} \)
\( R = \text{radius i den omskrevne cirkel} \)
Sinusrelationen |
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\( \frac{a}{\sin \left( A \right)} = \frac{b}{\sin \left( B \right)} = \frac{c}{\sin \left( C \right)} = 2 \cdot R \) \( \frac{\sin \left( A \right)}{a} = \frac{\sin \left( B \right)}{b} = \frac{\sin \left( C \right)}{c} = \frac{1}{2 \cdot R} \) \( R = \text{radius i den omskrevne cirkel} \) | |
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Cosinusrelationerne |
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\( a^2 = b^2 + c^2 - 2 \cdot b \cdot c \cdot \cos \left( A \right) \) \( b^2 = a^2 + c^2 - 2 \cdot a \cdot c \cdot \cos \left( B \right) \) \( c^2 = a^2 + b^2 - 2 \cdot a \cdot b \cdot \cos \left( C \right) \) \( \cos \left( A \right) = \frac{b^2 + c^2 - a^2}{2 \cdot b \cdot c} \) \( \cos \left( B \right) = \frac{a^2 + c^2 - b^2}{2 \cdot a \cdot c} \) \( \cos \left( C \right) = \frac{a^2 + b^2 - c^2}{2 \cdot a \cdot b} \) | |
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Tangensrelationerne |
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\( \tan \left( A \right) = \frac{\sin \left( B \right) \cdot a}{c - \cos \left( B \right) \cdot a} = \frac{\sin \left( C \right) \cdot a}{b - \cos \left( C \right) \cdot a} \) \( \tan \left( B \right) = \frac{\sin \left( A \right) \cdot b}{c - \cos \left( A \right) \cdot b} = \frac{\sin \left( C \right) \cdot b}{a - \cos \left( C \right) \cdot b} \) \( \tan \left( C \right) = \frac{\sin \left( A \right) \cdot c}{b - \cos \left( A \right) \cdot c} = \frac{\sin \left( B \right) \cdot c}{a - \cos \left( b \right) \cdot c} \) | |
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