Examples of Equations and Relationships Taken from "New Advances in Trigonometry : New Quadratic Equation Relationships to All-Integer Pythagorean Triangles

Contains over 70 equations (on its first page) that relate directly to the quadratic equation and its varied relationships with All-Integer Pythagaorean triangle sides, including: one equation and three unknowns(with several different solutions provided), Pythagorean triangles having sines and cosines(of the first order) on all three sides, Pythagorean triangles having a, b, and c (where a squared + b squared = c squared ) on each side, Pythagorean triangles which contain formulas that can be just ADDED together to gets its hypotenuse value( with equations and procedures that convert one type of Pythagorean triangle to another as cited above), Multiple General Equations for developing an INFINITE number of Pythagorean triangles for (1) any integer equal to or greater than the integer 3 ( including up to 50 or more All-Integer Pythagorean triangles having common sides), (2) Pythagorean triangles whose sides can be ADDED together to get its hypotenuse, (3) Pythagorean triangles that have sines and cosines on all three sides, and (4) Pythagorean triangles that have a, b, and c, where a squared + b squared = c squared. Plus 3 examples which show how (valid Pythagorean All-Integer) data given for two of its legs are used to obtain corresponding hypotenuse lengths WITHOUT the use of a square root operation. Three UNITY equations are given, that when multiplied by almost any algebraic or trigonometric equation the resultant becomes one side of an All-Integer Pythagorean triangle(All 2 sides are represented here). Four additional parameters are given for the normal quadratic equation with several associated test equations which show (verify) valid determinations of the four additional parameters. One page of New Trigonometric Identities in the Q (squared) = 2XY form, Selected Identities and more General Equations for developing Pythagorean triangles having ALL-Integers on each side, Two sets of examples providing ALL-integer Triangle sides for quadratic equations and converting Quadratic Equation Coefficients to 3 unknowns in a Single Equation. Three different equations each with several examples of using ONLY angle data to obtain Pythagorean triangle sides, plus a summary of Principles to be used for Developing and Solving for three unknowns in a single equation.This book contains one or more pages of examples of using each combination of equations plus one or more pages of problems where both teacher and student can exercise his or her newly acquired knowledge. These pages of examples illustrate examples what is expected in regard to the problems given.Gardner, Colin is the author of 'Examples of Equations and Relationships Taken from "New Advances in Trigonometry : New Quadratic Equation Relationships to All-Integer Pythagorean Triangles', published 2002 under ISBN 9780972034807 and ISBN 0972034803.