Page 1: Formulas and Examples of the Law of Cosines

The first page introduces the fundamental formulas of the twierdzenie cosinusów and provides examples of its application in solving triangles.

Definition: The Law of Cosines states that in a triangle with sides a, b, and c, and angles A, B, and C opposite these sides respectively, the following equations hold: a² = b² + c² - 2bc cos A b² = a² + c² - 2ac cos B c² = a² + b² - 2ab cos C

These formulas allow us to calculate unknown sides or angles in a triangle when we have sufficient information about the other elements.

Example: One problem demonstrates how to use the law of cosines to find the length of a side in a triangle with two known sides (5 and 4) and a known angle (120°).

The solution involves substituting the known values into the formula and solving for the unknown side. This example illustrates the practical application of twierdzenie cosinusów zadania.

Highlight: The page also includes a useful trigonometric identity: cos 120° = cos (180° - 60°) = -cos 60°. This identity is crucial for solving problems involving obtuse angles.

The page concludes with additional examples, demonstrating how to calculate angles using the law of cosines when all side lengths are known. These examples are excellent practice for students preparing for twierdzenie cosinusów zadania maturalne.