Trigonometry Ratios Table
Exact values for sin, cos and tan at standard angles (0°, 30°, 45°, 60°, 90°) and beyond. Features an interactive unit circle, real-time angle calculator, √0–√4 memory pattern, and SOHCAHTOA rules.
ESSENTIAL EXACT VALUES (0° – 90°)
| Angle (θ) | Radians | sin θ | cos θ | tan θ |
|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 |
| 30° | π/6 | 1/2 | √3 / 2 | 1/√3 |
| 45° | π/4 | √2 / 2 | √2 / 2 | 1 |
| 60° | π/3 | √3 / 2 | 1/2 | √3 |
| 90° | π/2 | 1 | 0 | — |
Click any row to inspect it on the unit circle →
REAL-TIME ANGLE CALCULATOR
THE √0 → √4 MEMORY TRICK
For sin θ, count from 0 to 4, take the square root, and divide by 2:
cos θ is simply sin in reverse order: cos 0° = √4/2 = 1, cos 90° = √0/2 = 0.
Save exact values and unit circle for study or revision
INTERACTIVE UNIT CIRCLE
SOHCAHTOA DEFINITIONS
Key identities: tan θ = sin θ / cos θ · sin²θ + cos²θ = 1
WHY 30°, 45° AND 60°?
Equilateral Triangle (30°, 60°)
Bisect an equilateral triangle of side length 2. The base splits to 1, and Pythagoras gives a height of √3. Thus sin 30° = 1/2 and sin 60° = √3/2 exactly.
Isosceles Right Triangle (45°)
A square of side 1 cut diagonally has a hypotenuse of √2. Thus sin 45° = cos 45° = 1/√2 = √2/2 exactly.
Trigonometry Ratios Table — Full Reference (0° to 360°)
mathsolvers.io/tables/trig-ratios/
All Standard Angles (0° to 360°)
Click any row to view on unit circle
| Angle | Radians | sin θ | cos θ | tan θ | sin (decimal) | cos (decimal) |
|---|---|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 | 0.0000 | 1.0000 |
| 30° | π/6 | 1/2 | √3 / 2 | 1/√3 | 0.5000 | 0.8660 |
| 45° | π/4 | √2 / 2 | √2 / 2 | 1 | 0.7071 | 0.7071 |
| 60° | π/3 | √3 / 2 | 1/2 | √3 | 0.8660 | 0.5000 |
| 90° | π/2 | 1 | 0 | — | 1.0000 | 0.0000 |
| 120° | 2π/3 | √3 / 2 | −1/2 | −√3 | 0.8660 | -0.5000 |
| 135° | 3π/4 | √2 / 2 | −√2 / 2 | −1 | 0.7071 | -0.7071 |
| 150° | 5π/6 | 1/2 | −√3 / 2 | −1/√3 | 0.5000 | -0.8660 |
| 180° | π | 0 | −1 | 0 | 0.0000 | -1.0000 |
| 210° | 7π/6 | −1/2 | −√3 / 2 | 1/√3 | -0.5000 | -0.8660 |
| 225° | 5π/4 | −√2 / 2 | −√2 / 2 | 1 | -0.7071 | -0.7071 |
| 240° | 4π/3 | −√3 / 2 | −1/2 | √3 | -0.8660 | -0.5000 |
| 270° | 3π/2 | −1 | 0 | — | -1.0000 | 0.0000 |
| 300° | 5π/3 | −√3 / 2 | 1/2 | −√3 | -0.8660 | 0.5000 |
| 315° | 7π/4 | −√2 / 2 | √2 / 2 | −1 | -0.7071 | 0.7071 |
| 330° | 11π/6 | −1/2 | √3 / 2 | −1/√3 | -0.5000 | 0.8660 |
| 360° | 2π | 0 | 1 | 0 | 0.0000 | 1.0000 |
Highlighted rows indicate standard exact values essential for secondary school & A-level exams.