law of cosines

noun

, Trigonometry.

1. a law stating that the square of a side of a plane triangle is equal to the sum of the squares of the other two sides minus twice the product of the other sides multiplied by the cosine of the angle between them.
2. a law stating that the cosine of an arc of a spherical triangle equals the sum of the product of the cosines of the other two arcs added to the product of the sines of the other two arcs multiplied by the cosine of the angle between them.

Example Sentences

The haversine formula is a re-formulation of the spherical law of cosines, but the formulation in terms of haversines is more useful for small angles and distances.

From Scientific American

Larry Eisenberg captured the moment with this limerick: With the law of cosines, I see, The angle opposite side 3 Is one eighty degrees The question’s a tease, A triangle like that can’t be.

From New York Times