Trigonometri

Sinusrelationerne

\(\frac{sin(A)}{a} = \frac{sin(B)}{b} = \frac{sin(C)}{c}\) eller \(\frac{a}{sin(A)} = \frac{b}{sin(B)} = \frac{c}{sin(C)}\)

Trekantens areal

\(T = \frac{1}{2} \cdot ab \cdot sin(C) = \frac{1}{2} \cdot ac \cdot sin(B) = \frac{1}{2} \cdot bc \cdot sin(A)\)

Cosinusrelationerne

• \(cos(A) = \frac{b^2 +c^2 -a^2}{2bc}\) eller \(a^2 = b^2 +c^2 -2bc \cdot cos(A)\)
• \(cos(B) = \frac{a^2 +c^2 -b^2}{2ac}\) eller \(b^2 = a^2 +c^2 -2ac \cdot cos(B)\)
• \(cos(C) = \frac{a^2 +b^2 -c^2}{2ab}\) eller \(c^2 = a^2 +b^2 -2ab \cdot cos(C)\)

Beregning af stykker i den almindelige trekant