Unit Circle Lab
An interactive unit circle. Drag a point on the circumference and read the angle in unit circle radians and degrees, plus the fraction of a turn. Coordinates show sin and cos on the unit circle, with the reference right triangle drawn in. Snap to 0°, 30°, 45°, 60°, 90° and the matching radian measures. Free, no login, ready for a classroom projector.
Who·Algebra 2 and precalculus on a projector or iPad
Teacher tip
Project this page and tap Full screen. It opens at 45°, π/4, one eighth of a turn, with cosine and sine both √2/2. Drag the black thumb — Snap is on, so it catches 30°, 60°, and 90°, the same places as π/6, π/3, and π/2. Stop at the top: 90°, π/2, one quarter turn, coordinates (0, 1). The flat side of the triangle is adjacent, cosine. The upright side is opposite, sine. Switch the big readout to Radians. Tap All six and slide toward 90°: tangent grows, then reads undefined on the axis. Tap Reset to return to 45°. One idea fits in five minutes.
Drag the point around the circle. The horizontal side is cosine. The vertical side is sine.
Degrees
45°
Radians
π/4
1/8 turn
cos θ
√2/2
sin θ
√2/2
(√2/2, √2/2)
Quadrant I
45°, π/4 radians, 1/8 turn. Coordinates (√2/2, √2/2).
Snap catches 0°, 30°, 45°, 60°, 90°, and the rest of that family — the same places as π/6, π/4, π/3, and π/2. Arrows move one degree, or the next common angle when Snap is on. Shift plus an arrow moves 15°. Escape clears.