Trigonometric Ratios
Reference table showing trigonometric function values for common angles.
Trigonometric Ratios for Common Angles
| Angle (°) | Angle (rad) | sin | cos | tan | cot | sec | csc |
|---|---|---|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 | undef | 1 | undef |
| 30° | π/6 | 1/2 | √3/2 | √3/3 | √3 | 2√3/3 | 2 |
| 45° | π/4 | √2/2 | √2/2 | 1 | 1 | √2 | √2 |
| 60° | π/3 | √3/2 | 1/2 | √3 | √3/3 | 2 | 2√3/3 |
| 90° | π/2 | 1 | 0 | undef | 0 | undef | 1 |
| 120° | 2π/3 | √3/2 | -1/2 | -√3 | -√3/3 | -2 | 2√3/3 |
| 135° | 3π/4 | √2/2 | -√2/2 | -1 | -1 | -√2 | √2 |
| 150° | 5π/6 | 1/2 | -√3/2 | -√3/3 | -√3 | -2√3/3 | 2 |
| 180° | π | 0 | -1 | 0 | undef | -1 | undef |
| 270° | 3π/2 | -1 | 0 | undef | 0 | undef | -1 |
| 360° | 2π | 0 | 1 | 0 | undef | 1 | undef |
Definitions
$$\sin θ = {\text"opposite"}/{\text"hypotenuse"}$$
$$\cos θ = {\text"adjacent"}/{\text"hypotenuse"}$$
$$\tan θ = {\text"opposite"}/{\text"adjacent"} = {\sin θ}/{\cos θ}$$
$$\cot θ = {\cos θ}/{\sin θ}$$
$$\sec θ = 1/{\cos θ}$$
$$\csc θ = 1/{\sin θ}$$