Eliminating The xy Term
| Autor: | Joseph V. Roberti |
|---|---|
| Rok vydání: | 1979 |
| Předmět: | |
| Zdroj: | The Mathematics Teacher. 72:695-700 |
| ISSN: | 2330-0582 0025-5769 |
| Popis: | computes sin and cos by Using the half angle formulas, and obtains the rotation equations (1) = ' cos y' sin and (2) y = y' sin + y9 cos e. The student then substitutes these ex pressions for and y in the general equa tion to transform it into one Without an xy term. . V. Yefimov of Moscow State Univer sity in his book, Quadratic Forms and Ma trices, has simplified the process consid erably by means of matrix transformations. Some calculus texts use a modified form of this approach, but even with the use of eigenvalues and eigenvectors, the degree of difficulty still tests the capabilities of the average calculus students, and hence, many instructors give it token attention or skip it altogether. I propose a process that brings the xy term elimination within the reach of more high school mathematics students. To begin, the student should know that the equation of a line perpendicular to a given line can be obtained by switching the coefficients of the variaoles and negating one of them. That is. |
| Databáze: | OpenAIRE |
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