Plane and Spherical Trigonometry

Excerpt from Plane and Spherical Trigonometry

This book is designed for those who wish to master the fundamental principles of Trigonometry and its most important applications. It is adapted to the use of colleges and high schools.

The proofs of formulas are simple but rigorous. The use of directed lines is consistent; the directions of such lines in the figures are usually indicated by arrowheads, and these lines are always read from origin to end. Both trigonometric ratios and trigonometric lines are employed, but at first the ratios are used exclusively until they have become fixed in the mind and have been made familiar by use in the solution of right triangles.

The distinction between identities and equations is recognized in definition, notation, and treatment. The solution of trigonometric equations is scientific and complete. The trigonometric ratios are defined in pairs as reciprocals of each other both to aid the memory and to emphasize one of the most important of their fundamental relations. The addition formulas are proved for positive or negative angles of any quadrant, and from them are deduced the other formulas concerning the functions of two or more angles. When two or more figures are used in a proof, the same phraseology always applies to each figure.

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