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The directions on a compass, the principal winds, half-winds, quarter-winds, etc, all correspond to angles that result of starting with a basic North-East-South-West compass rose and iteratively bisecting directions. What are the values of sine and cosine of the angles that correspond to these directions?

Compass Rose

Mike Pierce
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  • Note: the argument of $\sin$ is an angle, not a direction. So you need two directions, not one, to get a sine value. Typically, we often define the base direction as “east” when we draw the plane in the usual fashion, but here it seems like you should be specific. – Thomas Andrews Oct 03 '21 at 21:36
  • @ThomasAndrews Your'e saying we need to designate a direction as $0^\circ$ and say that we're measuring either clockwise or counterclockwise, yeah? I think folks outside of math who actually navigate use North as $0^\circ$ and measure clockwise? Either way, I'm hoping anyone who finds this post looking for an answer already knows that detail, and just needs the math in the duplicate target. – Mike Pierce Oct 03 '21 at 21:48

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