Trigonometry formulas are mathematical expressions that relate the angles of a triangle to the ratios of its sides, and they are fundamental to various fields such as geometry, physics, and engineering. Some of the most commonly used trigonometric identities include the Pythagorean identities. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.