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  • 2 - Trigonometry, the Foundation of Coordinate Theory

  • Don Koks
  • Book:
    Rotation Sequences and the Theory of Vectors and Coordinates
    Published online:
    17 April 2025
    Print publication:
    24 April 2025, pp 7-38

  • Summary

    Trigonometry is the basis of the book’s subject. I begin with length and angle, and then generalise to coordinates. This requires the important idea of a directed angle, which enables us to relate the sine and cosine of an angle to coordinates in any given orientation of a set of axes. I discuss the details of inverting the sine/cosine/tangent functions, and introduce a new function name to replace the inappropriate name “atan2” that often appears in the literature. The chapter ends with examples of calculating bearing and elevation.