Trigonometry Angles—Pi/15

Author

Eric W. Weisstein
October 9, 2007

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Trigonometry/TrigonometryAnglesPi15.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/TrigonometryAnglesPi15.html.

©2007 Wolfram Research, Inc. except for portions noted otherwise

Values

a=With[{n=15},Select[Range[n/2],GCD[#,n]==1&]]

<<Utilities`Simplify`

(values=Flatten[Map[{#,ToRadicals@SqrtSimplify[ExpandAll[FullSimplify[RootReduce[Developer`TrigToRadicals[#]]]]]}&,Transpose[Through[{Cos,Cot,Csc,Sec,Sin,Tan}[#Pi/15]]&/@a],
{2}],1])//ColumnForm

Check

Chop[Subtract@@@N[values]]