Drag on the circle to set θ · arrow keys nudge (Shift = 15°) · values beyond the view are clipped.
All six conventions side by side (signed values)
Click a column to make it the active convention. The outlined cell in each column is the segment that equals the Radius. Negative values mean the segment points the other way (θ outside the first quadrant).
Unwrapped around the circle (0° … 360°)
How to read this
In this lab, Radius is a custom geometric label: it is whichever trig value you choose, and that value is the length of one side of the right triangle. Standard definitions never change: SIN = Opp/Hyp, COS = Adj/Hyp, TAN = Opp/Adj, SEC = 1/COS, CSC = 1/SIN, COT = 1/TAN.
There are only three ways to normalize a triangle: Hypotenuse = 1 (Radius = SIN → Opposite, or COS → Adjacent), Adjacent = 1 (Radius = SEC → Hypotenuse, or TAN → Opposite) and Opposite = 1 (Radius = CSC → Hypotenuse, or COT → Adjacent). The scale factor k is 1, 1/COS(θ) or 1/SIN(θ), and every side is simply k × (Adj, Opp, Hyp) of the unit-circle triangle — which keeps everything consistent in all four quadrants.
With Hypotenuse = 1 and Radius = SIN(θ), the Radius and the Opposite side coincide because Radius was defined that way — it is not the conventional unit-circle radius, which is the hypotenuse.