Quadrantal Angle

Author

Eric W. Weisstein
August 12, 2026

This notebook downloaded from https://mathworld.wolfram.com/notebooks/Trigonometry/QuadrantalAngle.nb.

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

©2026 Wolfram Research, Inc. except for portions noted otherwise

Illustration

The terminal sides of quadrantal angles lie on the coordinate axes.

Module[{angleColor, labelBackground, neutral, points}, 
  neutral = LightDarkSwitched[Black, White]; angleColor = Blue; 
   labelBackground = LightDarkSwitched[White, Black]; points = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}}; 
   Graphics[{Directive[neutral, Dashing[{0.02, 0.02}]], Circle[], Directive[neutral, Dashing[{}], 
      AbsoluteThickness[1.5]], Line[{{-1.25, 0}, {1.25, 0}}], Line[{{0, -1.25}, {0, 1.25}}], 
     Directive[angleColor, AbsoluteThickness[3]], (Line[{{0, 0}, #1}] & ) /@ points, 
     Directive[angleColor, PointSize[0.02]], Point[points], 
     Text[Style["0", 16, neutral, Background -> labelBackground, FontFamily -> "Times"], 
      {1.08, 0.12}], Text[Style["π/2", 16, neutral, Background -> labelBackground, 
       FontFamily -> "Times"], {0.15, 1.08}], Text[Style["π", 16, neutral, 
       Background -> labelBackground, FontFamily -> "Times"], {-1.08, 0.12}], 
     Text[Style["3π/2", 16, neutral, Background -> labelBackground, FontFamily -> "Times"], 
      {0.22, -1.08}]}]]