law of cosines

English

Noun

law of cosines (uncountable)

1. (trigonometry) A generalization of the Pythagorean theorem that relates the lengths of the sides of a triangle to the cosine of one of its angles.

Usage notes

Let a, b, and c be the lengths of the sides of a triangle opposite angles A, B, and C. The law of cosines states

$a^{2}=b^{2}+c^{2}-2bc\cos {A}$

$b^{2}=a^{2}+c^{2}-2ac\cos {B}$

$c^{2}=a^{2}+b^{2}-2ab\cos {C}$.

Synonyms

• cosine formula
• cosine law
• cosine rule

Translations

statement

• Danish: cosinusrelationen c
• Finnish: kosinilause
• German: Kosinussatz m
• Hungarian: koszinusztétel (hu)
• Italian: teorema del coseno m
• Romanian: teorema cosinusului f (definite)
• Tagalog: kasinwaying batas

See also

• law of sines