Unit Circle Explorer
Unit Circle Explorer
Explore how angle measure maps to coordinates, signs, and right-triangle relationships on the unit circle.
(°)
Values & Structure
Angle45°
QuadrantQI
Reference angle45°
cos θ√2/2
sin θ√2/2
tan θ1
On the unit circle, a point at angle θ has coordinates (cos θ, sin θ). The reference triangle has adjacent |cos θ|, opposite |sin θ|, and hypotenuse 1.
Try this:
- Turn off “Snap to special angles” and slide 0°→360°. When does tan θ become undefined?
- Switch to radians and locate π/3. What are cos θ and sin θ there?
- Find all angles with sin θ = 1/2. What pattern do you notice?