What is the cosine rule?

Cosine's rule is a formula commonly used in trigonometry to determine certain aspects of a false triangle when other key parts of this triangle are known or otherwise can be determined. It is an effective extension of the Pythagorean sentence, which usually works only with true triangles and states that the square of the hypotene triangle equals squares of the other two sides when it adds (c 2 2 2 ). The cosine rule is an extension of this mathematical principle, which makes it effective for irregular triangles and states that with regard to a certain angle with a square side of the triangle, on the other hand, it equals squares of the other two sides, minus two sides occur together with the sponge (c -2ab cosc, where C is the opposite side of C).

Although many modern mathematical sources give credits to create a cosine government to a Muslim mathematician named Al-KAshi, there is also evidence that suggests that an ancient Greek mathematician Euclid invented a similar prince. Much of the modern algebra and trigonometry comes from the efforts of Muslims during the European dark age and around the 15th century al-Kashi codified the formula in a way that is still understood to this day. In France, the rule is even referred to as Le Theorème d'Al-kashi or "Theor Al-Kashi."

In general, the cosine rule is used in triangulation and many other practical trigonometry applications. This is particularly useful in systems where the lengths of all three sides are known or can be determined to determine the level of angles in the triangle. The cosine rule can also be used to create one side of the triangle, if the lengths of the other two sides are known, as well as the angle opposite this side.

As the cosine rule deals with triangles consisting of threeEqual parties and their angles, usually only work in the field of Euclidean geometry. Different versions of the cosine rule can be used for non -enforcement geometry, such as spherical geometry and hyperbolic geometry. In these systems, the triangle is determined by three points in the curved area and lines, usually curved lines that connect them. The hyperbolic law of the cosines and the spherical law of the cosines works similarly to the Euclidean Kosine government, because it can allow someone to create three triangle angles if it knows three sides. Unlike the Euclidean Kosine rules, however, these non -Euclidean laws can also allow someone to determine the size of the three sides of the triangle if they know three angles.