Algebra, Parabola, and Trigonometric Equations Which Can Be Used on Sides of Right Triangles

Provides new parameters for the quadratic equation such that two dozen or more trigonometric equations, using these same parameters, provide identical results. Twenty-two of these trigonometric equations have six different (looking) coefficients which make them all equal to one quadratic equation. Each equation using these same parameters has three sets of new parameters which make them so theycan be on sides of right triangles, with six sets that will do this is included. Each quadratic equation, having an integer solution, has also a Pythagorean equation which has identical answers. Equations to this is provided. One set of data is provided that makes this all possible, with the three answers, one for each side, being provided. Non-integer solutions are also possible. Each set of equations, or integers, on the sides of right triangles, can be put into a parabolic form, that is, what you see on the two legs of a right triangle can be "added" together to obtain the correct equation or integer on its hypotenuse. These three new quadratic (dependent) coefficients can be produced by four "independent" variables, with criteria on how to use them is provided. Conversion equation between the three and four types of new parameters is provided. Equations to make many new parabolic equations is provided with one examplebeing provided. A table of over a dozen different algebra equations which have two or three different trigonometric equations which have equal answers is shown, with angle criteria to ensure that this is true. Six conventional sets of normal trigonometric equations which can easily be put on sides on right triangles is provided, along with four sets containing sines and cosines on each triangle side but with different coefficients. Two examples showing how to convert normal quadratic equation coefficients to the three new coefficients is provided, along with answers. A third quadratic equation is given, only with answers. Algebraic equation conversions to each quadratic equation is provided. Next, parameters which define five different (data) variations for each algebra and trigonometric is provided with one (same) answer for each, making 15 different solutions. Five different trigonometric equations using these same new quadratic coefficients are provided, with all having the same identical answers as shown. Next, one set of trigonometric equations is shown on the sides of two different right triangles, each with different coefficients. What follows is a table of (equation) coefficients which can be expanded both in the horizontal as well as in the vertical direction to be as large as one desires, based upon any two (desired) selected sets of data. Equations to do this are provided. A special computer program which is required to compute these (and any future) coefficients is provided. This program has the capability to produce 3X3 tables of Pythagorean triples which meets a^2 + b^2 = c^2 criteria in both the horizontal as well as in the vertical direction. A table of these is provided. A set of equations is provided to convert 2nd order algebraic equations which are on the sides of a right triangle to parabolic, quadratic and one having sines and cosines on each (triangle) side, is provided. One example of using sines and cosines on a right triangle side to convert ANY other set of equations or integers to become a new set of (similar) equations or integers is also provided, with one example.Gardner, Colin is the author of 'Algebra, Parabola, and Trigonometric Equations Which Can Be Used on Sides of Right Triangles', published 2006 under ISBN 9780972034876 and ISBN 0972034870.