Matrices and Trigonometry (ePub)

Matrices and Determinants were discovered and developed in the eighteenth and nineteenth centuries. Initially, their development dealt with transformation of geometric objects and solution of systems of linear equations. Historically, the early emphasis was on the determinant, not the matrix. In modern treatments of linear algebra, matrices are considered first. We will not speculate much on this issue. The trigonometric functions (especially sine and cosine) for real or complex square matrices occur in solutions of second-order systems of differential equations. Trigonometry is a branch of mathematics that studies triangles, particularly right triangles. It deals with relationships between the sides and the angles of triangles and with the trigonometric functions, which describe those relationships, as well as describing angles in general and the motion of waves such as sound and light waves. Trigonometric concepts are used to minimize the amount of measuring . These concepts depend on the concepts of enlargement and similarity. Equiangular triangles have the same shape, but only in the special case of congruency they do have the same size. Any set of similar triangles has the invariant property of proportionality; that is, ratios of pairs of corresponding sides are in the same proportion. In the language of transformation geometry, for similar triangles, one triangle is an enlargement of another, or any triangle can be transformed into another by applying the same scale factor to each part of the triangle. In the case of a fractional scale factor the enlargement is, in fact, a reduction. It is hoped that the book would be highly useful for the students and teachers of mathematics. Students aspiring to successfully accomplish engineering and also those preparing for various competitive examinations are likely to find this book of much help.