The Pythagorean identity is sin2Ø + cos2Ø = 1. This is called the fundamental identity in trigonometry. Two other identities are 1+ tan2Ø = sec2Ø and 1+ cot2Ø = cosec2Ø.
A Pythagorean triple, also called a triplet, are any three numbers that go together to validly fulfill the Pythagorean theorem, a2 + b2 = c2. The Pythagorean theorem states that for any right angle triangle, the sum of the two shortest sides squared will be equal to the length of the hypotenuse, or
A Pythagorean triple is a set of three positive integers, (a, b, c), such that a right triangle can be formed with the legs a and b and the hypotenuse c. The most common Pythagorean triples are (3, 4, 5), (5, 12, 13), (8, 15, 17) and (7, 24, 25).
Hippassus of Meropontum discovered irrational numbers in the fifth century B.C., when he developed the Pythagorean theorum for right triangles and discovered that hypotenuse length could not always be expressed as a rational number. The Euclidean proof of irrational numbers did not appear until 300
The work-energy theorem is a generalized description of motion that states that the work done by the sum of all forces acting on an object is equal to the change in that object's kinetic energy. This principle of work and its relationship to kinetic energy is a core mechanical physics concept.
The base angle theorem says if two sides of a triangle are congruent, then the angles opposite those sides must also be congruent. The converse is also true. If two angles of a triangle are congruent, then the opposite sides must be also be congruent.
Examples of the squeeze theorem, g(x) ? f(x) ? h(x), show that if f(x) is always greater than g(x) and if f(x) is always less than h(x), then when g(x) is equal to h(x), f(x) must also be equal. Since f(x) always squeezes between g(x) and h(x), it must be equal when g(x) and h(x) are equal.
A linear pair of angles is always supplementary. This means that the sum of the angles of a linear pair is always 180 degrees. This is called the linear pair theorem.
The midpoint theorem is a theory used in coordinate geometry that states that the midpoint of a line segment is the average of its endpoints. Solving an equation using this method requires that both the x and y coordinates are known. This theorem can also be used in algebra and calculus.
The Pythagorean theorem states that when a triangle has a right angle and all three sides are squared, the longest side squared will equal the size of the smaller two sides squared and summed. It is usually expressed as a^2+b^2=c^2.