Unit Circle Explorer
Skill goal: connect angle, coordinates, and trig values.
Observe
Drag the gold point around the circle. Watch how the angle, the coordinates, and the trig values change.
Manipulate
Tip: drag the gold point. It snaps to special angles (30°, 45°, 60°, …).
Predict: Before you change it, what do you think will happen? If you drag the point to the second quadrant, what happens to the signs of cos θ and sin θ?
See
Angle
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Radians
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cos θ (x-coordinate)
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sin θ (y-coordinate)
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Quadrant
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Reference angle
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Explain
Why it works: A point on the unit circle is defined as (cos θ, sin θ) — its x-coordinate is the cosine and its y-coordinate is the sine of the angle. The dashed lines drop the point straight onto each axis so you can read both values directly. The reference angle is the acute angle between the radius and the x-axis; it tells you the size of the trig values, while the quadrant tells you their signs.
Challenge
1. Find the angle θ in Quadrant II with sin θ = 1/2. Enter θ in degrees.
2. If sin θ = −1 and 0° ≤ θ < 360°, what is θ (in degrees)?