To determine the cosecant of θ on the unit circle:
From the center of the circle draw the radius corresponding to the angle θ.
Draw tangent lines to the circle at points (0,1) and (0,-1).
Extend the radius from Step 1 so that it intersects one of those tangents.
The distance from the center to the intersection point from Step 3 is the cosecant of your angle θ.
If there's no intersection point, the cosecant of θ is undefined (this happens when sin θ = 0).
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