Unit Circle Chart — All Values, Angles & Coordinates A complete reference for the unit circle. The unit circle is the circle of radius 1 centered at the origin. Any point on it has coordinates (cos θ, sin θ). This sheet covers every standard angle in degrees and radians, plus the exact values of sine, cosine, and tangent.
Unit Circle Definition Equation of the Unit Circle
x 2 + y 2 = 1 x^2 + y^2 = 1 x 2 + y 2 = 1 Coordinate on Unit Circle
( x , y ) = ( cos θ , sin θ ) (x, y) = (\cos\theta,\ \sin\theta) ( x , y ) = ( cos θ , sin θ ) Pythagorean Identity
sin 2 θ + cos 2 θ = 1 \sin^2\theta + \cos^2\theta = 1 sin 2 θ + cos 2 θ = 1 Tangent
tan θ = sin θ cos θ \tan\theta = \frac{\sin\theta}{\cos\theta} tan θ = cos θ sin θ
Degrees ↔ Radians Degrees to Radians
θ rad = θ deg ⋅ π 180 \theta_\text{rad} = \theta_\text{deg} \cdot \frac{\pi}{180} θ rad = θ deg ⋅ 180 π Radians to Degrees
θ deg = θ rad ⋅ 180 π \theta_\text{deg} = \theta_\text{rad} \cdot \frac{180}{\pi} θ deg = θ rad ⋅ π 180 Full Circle
360 ° = 2 π rad 360° = 2\pi \text{ rad} 360° = 2 π rad Half Circle
180 ° = π rad 180° = \pi \text{ rad} 180° = π rad Quarter Circle
90 ° = π 2 rad 90° = \tfrac{\pi}{2} \text{ rad} 90° = 2 π rad Sine Values at Standard Angles sin 30° = sin π/6
sin π 6 = 1 2 \sin\tfrac{\pi}{6} = \tfrac{1}{2} sin 6 π = 2 1 sin 45° = sin π/4
sin π 4 = 2 2 \sin\tfrac{\pi}{4} = \tfrac{\sqrt{2}}{2} sin 4 π = 2 2 sin 60° = sin π/3
sin π 3 = 3 2 \sin\tfrac{\pi}{3} = \tfrac{\sqrt{3}}{2} sin 3 π = 2 3 sin 90° = sin π/2
sin π 2 = 1 \sin\tfrac{\pi}{2} = 1 sin 2 π = 1 sin 270° = sin 3π/2
sin 3 π 2 = − 1 \sin\tfrac{3\pi}{2} = -1 sin 2 3 π = − 1 Cosine Values at Standard Angles cos 30° = cos π/6
cos π 6 = 3 2 \cos\tfrac{\pi}{6} = \tfrac{\sqrt{3}}{2} cos 6 π = 2 3 cos 45° = cos π/4
cos π 4 = 2 2 \cos\tfrac{\pi}{4} = \tfrac{\sqrt{2}}{2} cos 4 π = 2 2 cos 60° = cos π/3
cos π 3 = 1 2 \cos\tfrac{\pi}{3} = \tfrac{1}{2} cos 3 π = 2 1 cos 90° = cos π/2
cos π 2 = 0 \cos\tfrac{\pi}{2} = 0 cos 2 π = 0 cos 180° = cos π
cos π = − 1 \cos\pi = -1 cos π = − 1 cos 270° = cos 3π/2
cos 3 π 2 = 0 \cos\tfrac{3\pi}{2} = 0 cos 2 3 π = 0 Tangent Values at Standard Angles tan 30° = tan π/6
tan π 6 = 3 3 \tan\tfrac{\pi}{6} = \tfrac{\sqrt{3}}{3} tan 6 π = 3 3 tan 45° = tan π/4
tan π 4 = 1 \tan\tfrac{\pi}{4} = 1 tan 4 π = 1 tan 60° = tan π/3
tan π 3 = 3 \tan\tfrac{\pi}{3} = \sqrt{3} tan 3 π = 3 tan 90° = tan π/2
tan π 2 is undefined \tan\tfrac{\pi}{2} \text{ is undefined} tan 2 π is undefined tan 270° = tan 3π/2
tan 3 π 2 is undefined \tan\tfrac{3\pi}{2} \text{ is undefined} tan 2 3 π is undefined Quadrant Signs (ASTC: All Students Take Calculus) Quadrant I (0° to 90°)
sin > 0 , cos > 0 , tan > 0 ( All positive ) \sin > 0,\ \cos > 0,\ \tan > 0 \quad(\text{All positive}) sin > 0 , cos > 0 , tan > 0 ( All positive ) Quadrant II (90° to 180°)
sin > 0 , cos < 0 , tan < 0 ( Sine positive ) \sin > 0,\ \cos < 0,\ \tan < 0 \quad(\text{Sine positive}) sin > 0 , cos < 0 , tan < 0 ( Sine positive ) Quadrant III (180° to 270°)
sin < 0 , cos < 0 , tan > 0 ( Tangent positive ) \sin < 0,\ \cos < 0,\ \tan > 0 \quad(\text{Tangent positive}) sin < 0 , cos < 0 , tan > 0 ( Tangent positive ) Quadrant IV (270° to 360°)
sin < 0 , cos > 0 , tan < 0 ( Cosine positive ) \sin < 0,\ \cos > 0,\ \tan < 0 \quad(\text{Cosine positive}) sin < 0 , cos > 0 , tan < 0 ( Cosine positive ) Reciprocal Functions (csc, sec, cot) Cosecant
csc θ = 1 sin θ \csc\theta = \frac{1}{\sin\theta} csc θ = sin θ 1 Secant
sec θ = 1 cos θ \sec\theta = \frac{1}{\cos\theta} sec θ = cos θ 1 Cotangent
cot θ = cos θ sin θ = 1 tan θ \cot\theta = \frac{\cos\theta}{\sin\theta} = \frac{1}{\tan\theta} cot θ = sin θ cos θ = tan θ 1
