30° is π/6 radians; sin 60° = √3/2 ≈ 0.8660 and cos 135° = −√2/2 ≈ -0.7071.
| Degrees | Radians | Radians (decimal) | sin (exact) | cos (exact) | sin | cos |
|---|---|---|---|---|---|---|
| 0 | 0 | 0.0000 | 0 | 1 | 0.0000 | 1.0000 |
| 30 | π/6 | 0.5236 | 1/2 | √3/2 | 0.5000 | 0.8660 |
| 45 | π/4 | 0.7854 | √2/2 | √2/2 | 0.7071 | 0.7071 |
| 60 | π/3 | 1.0472 | √3/2 | 1/2 | 0.8660 | 0.5000 |
| 90 | π/2 | 1.5708 | 1 | 0 | 1.0000 | 0.0000 |
| 120 | 2π/3 | 2.0944 | √3/2 | −1/2 | 0.8660 | -0.5000 |
| 135 | 3π/4 | 2.3562 | √2/2 | −√2/2 | 0.7071 | -0.7071 |
| 150 | 5π/6 | 2.6180 | 1/2 | −√3/2 | 0.5000 | -0.8660 |
| 180 | π | 3.1416 | 0 | −1 | 0.0000 | -1.0000 |
| 210 | 7π/6 | 3.6652 | −1/2 | −√3/2 | -0.5000 | -0.8660 |
| 225 | 5π/4 | 3.9270 | −√2/2 | −√2/2 | -0.7071 | -0.7071 |
| 240 | 4π/3 | 4.1888 | −√3/2 | −1/2 | -0.8660 | -0.5000 |
| 270 | 3π/2 | 4.7124 | −1 | 0 | -1.0000 | 0.0000 |
| 300 | 5π/3 | 5.2360 | −√3/2 | 1/2 | -0.8660 | 0.5000 |
| 315 | 7π/4 | 5.4978 | −√2/2 | √2/2 | -0.7071 | 0.7071 |
| 330 | 11π/6 | 5.7596 | −1/2 | √3/2 | -0.5000 | 0.8660 |
| 360 | 2π | 6.2832 | 0 | 1 | 0.0000 | 1.0000 |
How it is computed
On a circle of radius 1, the point at angle θ has coordinates (cos θ, sin θ). Radians = degrees × π ÷ 180. Exact values come from the 30-60-90 and 45-45-90 triangles; the quadrant sets the sign (sine is negative below the x-axis, cosine left of the y-axis).
FAQ
How do I remember the signs in each quadrant?+
All, Students, Take, Calculus: all positive in quadrant I, sine in II, tangent in III, cosine in IV, counter-clockwise from 0°.
Why use radians instead of degrees?+
A radian is the angle whose arc equals the radius, so arc length is simply r × θ. Calculus formulas, like the derivative of sin x being cos x, only hold in radians.