NÁMSGÖGN · INTERACTIVE MATHEMATICS
One angle. Countless connections.
Turn an angle. See a wave. Find the connection.
Shared angle and radius
x ≈ 0.866 · y ≈ 0.5
Fictional setting · exact mathematics
02 / 09 · Explore freely
What do the point's coordinates tell us about the angle?
At 30° on the unit circle, y = 0.5. Predict x and y at 120° before turning the arm.
Values and relationship · model units
x = r cos θ · y = r sin θ
| x = r cos θ | 0.866 |
|---|---|
| y = r sin θ | 0.5 |
| sin θ | 0.5 |
| cos θ | 0.866 |
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Foundation check: explain coordinate signs in each quadrant and why division by radius removes the scale difference.
Your explanation stays only while the laboratory is open. No scores or proficiency assessment.