• I. N. Bronshtein
  • K. A. Semendyayev


Radian measure of angles. Besides the practical degree measure of angles, the radian or circular measure is also in use in theoretical considerations. A central angle α of an arbitrary circle subtended by an arc l is measured by the ratio of l to the radius r of the circle:
$$ \alpha =\frac{l}{r} $$


Trigonometric Function Hyperbolic Function Vector Diagram Spherical Triangle Fundamental Formula 


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  1. (1).
    There is no special symbol for a radian; the angle equal to α radians is denoted simply by α.Google Scholar
  2. (2).
    The angle α is measured from the fixed radius OA to the moving radius OC in the counter-clockwise direction (the positive direction).Google Scholar
  3. (1).
    The graph of the sine is the usual sine curve (see p. 111).Google Scholar
  4. (1).
    Values of the functions of angles expressed in radians can be obtain from the tables on pp. 61–65; they give the values of the functions for arguments contained between 0.00 and 1.60. If an angle falls beyond the limits of the table, we use the same rules and reducing formulas as for the angles measured in degrees, e.g., \( \textup{sin}(2\pi +x)=\textup{sin}\;x,\;\textup{sin}(2\pi-x)=-\textup{sin}\;x \).Google Scholar
  5. (1).
    The sign “+” or “−” before the radicals should be chosen according to the quadrant in which the angle lies.Google Scholar
  6. (1).
    (NK) are Newton’s binomial coefficients (see p. 193).Google Scholar
  7. (1).
    In the vibration theory this quantity is called the cyclic or circular frequency.Google Scholar
  8. (1).
    These formulas are true only for the principal values of the inverse trigonometric functions and the formulas in rectangular brackets are true only tor positive values of x (since the principal values lie in various intervals).Google Scholar
  9. (1).
    This formula holds also for non-integral values of n.Google Scholar
  10. (1).
    See p. 312.Google Scholar
  11. (1).
    Elementary information about hyperbolic functions analogous to those concerning trigonometric functions is collected under this title.Google Scholar
  12. (1).
    These relations can be deduced from the corresponding formulas for the trigonometric functions by means of a simple rule, see p. 232.Google Scholar
  13. (1).
    For the functions of a complex variable see pp. 592–595.Google Scholar

Copyright information

© Verlag Harri Deutsch, Zürich 1973

Authors and Affiliations

  • I. N. Bronshtein
  • K. A. Semendyayev

There are no affiliations available

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