A circle of radius 1 centred at the origin. Every angle θ corresponds to a point (cos θ, sin θ) on the circle.
Drag around the circle
θ = 45° = π/4
quadrant I
sin θ = y = 0.707
cos θ = x = 0.707
tan θ = sin/cos = 1
On the unit circle the point at angle θ is exactly (cos θ, sin θ). So cos is the x-coordinate, sin is the y-coordinate — drag the angle above and watch them. tan θ is the slope of that radius (y/x).
Your turn
What are the coordinates of the point at θ = 60° on the unit circle?
Why it matters
- It extends sin and cos to any angle, including past 90° and negative angles.
- Signs of sin/cos in each quadrant come straight from x and y signs.
- It's the bridge from triangle trig to the wave graphs of sin and cos.
Key angles
- 0°: (1, 0)
- 90°: (0, 1)
- 180°: (−1, 0)
- 270°: (0, −1)