Interactive geometry laboratory

One circle. Six functions. Three phases.

Explore where trigonometric identities come from—not just what to memorize.

Source Video: You Can Rebuild All of Trig From This One Circle

◉ Offline-ready · SVG geometry · Live calculations
Phase 01 · Shadow / Touch / Cut

The six trigonometric functions

Toggle any combination of the six constructions. Drag the white point on the circle or change θ to see the geometry update.

FIRST QUADRANT
↔ Drag the point on the circle to change θθ = 38° · Radius = 1

Angle control

Live
Select quadrant

Reference angle: 38° · All six values positive

38°0.663 rad
8°45°82°

Choose a quadrant, move the slider, or drag the point around the circle. Colored tangent and secant segments represent magnitudes; the numerical readouts show the signed function values. Angles stay at least 8° from the axes to avoid undefined or extremely large ratios.

Function visibility

Any combination
Three physical actions × two axes = six functions. “Shadow” uses coordinate projections, “Touch” measures along the tangent lines x = ±1 or y = ±1, and “Cut” measures the radial segments to those lines. Outside quadrant I, construction lines move to the tangent on the matching side of the circle, with signed values displayed above.
Sine / verticalCosine / horizontalTangentCotangentSecantCosecant