The Unit Circle
Grades 9–12 Trigonometry Circles
Draw a circle of radius 1 around the origin. Walk θ degrees around it from the right edge — the point you land on is (cos θ, sin θ). That's the whole unit circle: cos is the x, sin is the y.
The key stops
0° (1, 0) cos=1 sin=0
90° (0, 1) cos=0 sin=1
180° (−1, 0) cos=−1 sin=0
270° (0, −1) cos=0 sin=−1
360° back home
Why everything repeats
390° is just 30° plus a full lap — same point, same cos/sin. All trig functions loop every 360° (or 2π radians). Negative angles walk the circle clockwise.
The identity you get free
Every point (cos θ, sin θ) sits on a circle of radius 1, so by
Pythagoras:
cos²θ + sin²θ = 1 — the most-used
trig identity, straight off the picture.
Practice
At 90°, cos θ = ___
At 180°, cos θ = ___
sin 390° equals:
cos²θ + sin²θ = ___
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