Trigonometry
Values Table
Complete reference for sine, cosine, and tangent values from 0° to 360°, with radians and a calculator.
Trigonometry Calculator
| Degrees | Radians | sin θ | cos θ | tan θ |
|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 |
| 30° | π/6 | 1/2 | √3/2 | √3/3 |
| 45° | π/4 | √2/2 | √2/2 | 1 |
| 60° | π/3 | √3/2 | 1/2 | √3 |
| 90° | π/2 | 1 | 0 | undefined |
| 120° | 2π/3 | √3/2 | -1/2 | -√3 |
| 135° | 3π/4 | √2/2 | -√2/2 | -1 |
| 150° | 5π/6 | 1/2 | -√3/2 | -√3/3 |
| 180° | π | 0 | -1 | 0 |
| 210° | 7π/6 | -1/2 | -√3/2 | √3/3 |
| 225° | 5π/4 | -√2/2 | -√2/2 | 1 |
| 240° | 4π/3 | -√3/2 | -1/2 | √3 |
| 270° | 3π/2 | -1 | 0 | undefined |
| 300° | 5π/3 | -√3/2 | 1/2 | -√3 |
| 315° | 7π/4 | -√2/2 | √2/2 | -1 |
| 330° | 11π/6 | -1/2 | √3/2 | -√3/3 |
| 360° | 2π | 0 | 1 | 0 |
Key Trigonometric Identities
Pythagorean
sin²θ + cos²θ = 1
Tangent
tan θ = sin θ / cos θ
Reciprocal
csc θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ
Double Angle (sin)
sin 2θ = 2 sin θ cos θ
Double Angle (cos)
cos 2θ = cos²θ - sin²θ
Sum (sin)
sin(α + β) = sin α cos β + cos α sin β
Sum (cos)
cos(α + β) = cos α cos β - sin α sin β
Understanding the Unit Circle
The Unit Circle
A circle with radius 1 centered at the origin. For any angle θ, the coordinates of the point on the circle are (cos θ, sin θ).
Quadrant Signs
Q1 (0°-90°): All positive
Q2 (90°-180°): Only sin positive
Q3 (180°-270°): Only tan positive
Q4 (270°-360°): Only cos positive
Degrees to Radians
Multiply degrees by π/180.
180° = π radians
90° = π/2 radians
360° = 2π radians
Special Triangles
30-60-90 triangle: sides 1, √3, 2
45-45-90 triangle: sides 1, 1, √2
These give exact values for common angles.