Csc and Sec in Surds (original) (raw)

Julian D. A. Wiseman

Contents: values of Cosecant[α] = Cosec[α] = Csc[α] = 1/Sin[α] and Secant[α] = Sec[α] = 1/Cos[α], expressed in surds, for α=_n_×3° or α=_n_×5⅝°, _n_∈ℕ:Csc[0°], Csc[3°], Csc[5.625°], Csc[6°], Csc[9°], Csc[11.25°], Csc[12°], Csc[15°], Csc[16.875°], Csc[18°], Csc[21°], Csc[22.5°], Csc[24°], Csc[27°], Csc[28.125°], Csc[30°], Csc[33°], Csc[33.75°], Csc[36°], Csc[39°], Csc[39.375°], Csc[42°], Csc[45°], Csc[48°], Csc[50.625°], Csc[51°], Csc[54°], Csc[56.25°], Csc[57°], Csc[60°], Csc[61.875°], Csc[63°], Csc[66°], Csc[67.5°], Csc[69°], Csc[72°], Csc[73.125°], Csc[75°], Csc[78°], Csc[78.75°], Csc[81°], Csc[84°], Csc[84.375°], Csc[87°], and Csc[90°].

The table shows Cosecant[] = Cosec[] = Csc[] = 1/Sin[] and Secant[] = Sec[] = 1/Cos[] in surds, for angles that are integer multiples of 3° or of 5⅝° = 90°/16. The surds are derived from the table of values of Sin[] and Cos[] in surds, and are shown in several formats.

Help! Endeavours have been made to represent these values as simply as possible. But further simplifications would be welcomed, credit being given.

Errors: whilst the outputs have been tested, it is possible that errors remain. Please do test things before embedding them somewhere important—and if errors or possible improvements are found, tell the author.

Julian D. A. Wiseman, June 2008