Trigonometry Values Table
Complete table of sin, cos, tan, cosec, sec, cot values for 0°, 30°, 45°, 60°, 90° and beyond.
Standard Angle Values (Exact Form)
| Angle (°) | Radians | sin | cos | tan | cosec | sec | cot |
|---|---|---|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 | ∞ | 1 | ∞ |
| 30° | π/6 | 1/2 | √3/2 | 1/√3 | 2 | 2/√3 | √3 |
| 45° | π/4 | 1/√2 | 1/√2 | 1 | √2 | √2 | 1 |
| 60° | π/3 | √3/2 | 1/2 | √3 | 2/√3 | 2 | 1/√3 |
| 90° | π/2 | 1 | 0 | ∞ | 1 | ∞ | 0 |
| 120° | 2π/3 | √3/2 | −1/2 | −√3 | 2/√3 | −2 | −1/√3 |
| 135° | 3π/4 | 1/√2 | −1/√2 | −1 | √2 | −√2 | −1 |
| 150° | 5π/6 | 1/2 | −√3/2 | −1/√3 | 2 | −2/√3 | −√3 |
| 180° | π | 0 | −1 | 0 | ∞ | −1 | ∞ |
| 210° | 7π/6 | −1/2 | −√3/2 | 1/√3 | −2 | −2/√3 | √3 |
| 225° | 5π/4 | −1/√2 | −1/√2 | 1 | −√2 | −√2 | 1 |
| 240° | 4π/3 | −√3/2 | −1/2 | √3 | −2/√3 | −2 | 1/√3 |
| 270° | 3π/2 | −1 | 0 | ∞ | −1 | ∞ | 0 |
| 300° | 5π/3 | −√3/2 | 1/2 | −√3 | −2/√3 | 2 | −1/√3 |
| 315° | 7π/4 | −1/√2 | 1/√2 | −1 | −√2 | √2 | −1 |
| 330° | 11π/6 | −1/2 | √3/2 | −1/√3 | −2 | 2/√3 | −√3 |
| 360° | 2π | 0 | 1 | 0 | ∞ | 1 | ∞ |
Frequently asked questions
What are the standard angles in trigonometry?
The standard angles are 0°, 30°, 45°, 60°, and 90° (and their supplements/co-terminal equivalents). These angles have exact, simple values that can be memorised or derived from equilateral and right-isosceles triangles.
How do I remember sin and cos values for 0°, 30°, 45°, 60°, 90°?
Use the pattern: sin = √0/2, √1/2, √2/2, √3/2, √4/2 for 0°, 30°, 45°, 60°, 90°. Simplify each: 0, 1/2, 1/√2, √3/2, 1. cos values are the reverse (cos θ = sin(90°−θ)).
Why is tan 90° undefined?
tan θ = sin θ / cos θ. At 90°, cos 90° = 0, so the division is undefined (division by zero). Similarly, cosec 0° and cot 90° are undefined.
What is the difference between cosec, sec and cot?
cosec θ = 1/sin θ, sec θ = 1/cos θ, and cot θ = 1/tan θ = cos θ/sin θ. These are the reciprocal trigonometric functions. They are used in integration, physics and engineering.
What are co-terminal angles?
Co-terminal angles share the same terminal side. 0° and 360° are co-terminal (same as 720°, −360°, etc.). Adding or subtracting multiples of 360° gives co-terminal angles with identical trig values.