Unit Circle Explorer

📋 Teacher notes

• •Every point on the unit circle is (cos θ, sin θ) — that's not a coincidence to memorise, it's the actual definition. Drag the point and watch both coordinates update together.
• •The yellow line is always the point's x-coordinate (cos θ); the red line is always its y-coordinate (sin θ) — the 'projection' picture is the fastest way to see why sin and cos are just shifted copies of each other (90° out of phase).
• •The sign of sin θ and cos θ in each quadrant follows directly from which coordinates are positive/negative there — no need to memorise 'CAST' or similar mnemonics if students can see why it's true here.
• •Degrees and radians are just two different rulers measuring the same rotation — 360° and 2π radians are the same full turn. The toggle lets students build intuition for both before an exam forces a quick conversion.
• •The two graphs below are literally 'unroll the circle onto a line' — dragging the point around the circle traces out exactly the sine and cosine curves, in real time.