Trig Values Reference
The standard angles from 0° to 360°, in exact degrees and radians, with quadrant, reference angle, and all six trig function values — generated live from the degrees to radians converter and the trig function & identity calculator, not a separately hand-typed table.
Degrees, radians, quadrant, and reference angle
| Degrees | Radians | Quadrant | Reference angle |
|---|---|---|---|
| 0° | 0 | axis | 0° |
| 30° | π/6 | 1 (I) | 30° |
| 45° | π/4 | 1 (I) | 45° |
| 60° | π/3 | 1 (I) | 60° |
| 90° | π/2 | axis | 90° |
| 120° | 2π/3 | 2 (II) | 60° |
| 135° | 3π/4 | 2 (II) | 45° |
| 150° | 5π/6 | 2 (II) | 30° |
| 180° | π | axis | 0° |
| 210° | 7π/6 | 3 (III) | 30° |
| 225° | 5π/4 | 3 (III) | 45° |
| 240° | 4π/3 | 3 (III) | 60° |
| 270° | 3π/2 | axis | 90° |
| 300° | 5π/3 | 4 (IV) | 60° |
| 315° | 7π/4 | 4 (IV) | 45° |
| 330° | 11π/6 | 4 (IV) | 30° |
| 360° | 2π | axis | 0° |
All six trig function values
| Degrees | sin | cos | tan | csc | sec | cot |
|---|---|---|---|---|---|---|
| 0° | 0 | 1 | 0 | undefined | 1 | undefined |
| 30° | 0.5 | 0.866 | 0.5774 | 2 | 1.1547 | 1.7321 |
| 45° | 0.7071 | 0.7071 | 1 | 1.4142 | 1.4142 | 1 |
| 60° | 0.866 | 0.5 | 1.7321 | 1.1547 | 2 | 0.5774 |
| 90° | 1 | 0 | undefined | 1 | undefined | 0 |
| 120° | 0.866 | -0.5 | -1.7321 | 1.1547 | -2 | -0.5774 |
| 135° | 0.7071 | -0.7071 | -1 | 1.4142 | -1.4142 | -1 |
| 150° | 0.5 | -0.866 | -0.5774 | 2 | -1.1547 | -1.7321 |
| 180° | 0 | -1 | 0 | undefined | -1 | undefined |
| 210° | -0.5 | -0.866 | 0.5774 | -2 | -1.1547 | 1.7321 |
| 225° | -0.7071 | -0.7071 | 1 | -1.4142 | -1.4142 | 1 |
| 240° | -0.866 | -0.5 | 1.7321 | -1.1547 | -2 | 0.5774 |
| 270° | -1 | 0 | undefined | -1 | undefined | 0 |
| 300° | -0.866 | 0.5 | -1.7321 | -1.1547 | 2 | -0.5774 |
| 315° | -0.7071 | 0.7071 | -1 | -1.4142 | 1.4142 | -1 |
| 330° | -0.5 | 0.866 | -0.5774 | -2 | 1.1547 | -1.7321 |
| 360° | 0 | 1 | 0 | undefined | 1 | undefined |
"undefined" marks a division by zero — tangent and secant at 90° and 270°, cosecant and cotangent at 0°, 180°, and 360°. Values are rounded to four decimal places for display, matching every calculator on the site.
Why these seventeen angles
Five angles in the first quadrant — 0°, 30°, 45°, 60°, and 90° — have exact, memorable trig values built from two simple triangles: an isosceles right triangle for 45°, and a bisected equilateral triangle for 30° and 60°. Every other angle in the table is one of those five reflected into another quadrant, which is why the numbers repeat in size and only the sign (and occasionally which function plays which role) changes from one quadrant to the next.
Reading the two tables side by side is the fastest way to see the sign pattern in action: compare 30° to 150°, 210°, and 330° — the same reference angle of 30° and the same unsigned values throughout, with only the sign of sine and cosine changing to match the quadrant.
Frequently Asked Questions
Where do the numbers in this table come from?
Every value is computed live by the site's own trigonometry functions: the radians, quadrant, and reference angle come from the same convertAngle() logic behind the degrees to radians converter, and the sine, cosine, tangent, and their three reciprocals come from the same evaluateTrig() logic behind the trig function & identity calculator. Nothing here is a separately hand-typed table, so the two can never drift out of sync.
Why is tangent (and secant) blank at 90° and 270°?
Tangent is sine divided by cosine, and cosine is exactly 0 at 90° and 270° — dividing by zero has no defined result, so tangent is undefined at those two angles. Secant, the reciprocal of cosine, is undefined there for the identical reason. The table marks both as undefined rather than showing a made-up number.
Why are cosecant and cotangent blank at 0°, 180°, and 360°?
Cosecant is the reciprocal of sine, and cotangent is cosine divided by sine — both need sine in a denominator, and sine is exactly 0 at 0°, 180°, and 360°. The same division-by-zero logic that leaves tangent and secant undefined at the axis points along the x-axis leaves cosecant and cotangent undefined at the axis points along the y-axis.
What is the "reference angle" column?
The reference angle is the acute angle (always between 0° and 90°) between an angle's terminal side and the x-axis. It is the key to finding any angle's trig values from the first-quadrant values alone: look up the reference angle's sine, cosine, and tangent, then apply the sign that matches the original angle's quadrant.
Use it with
- Degrees to Radians Converter — convert any angle, not just the standard ones listed here, and read its quadrant and reference angle the same way.
- Trig Function & Identity Calculator — evaluate all six functions at any angle, with a live check of the Pythagorean identity.
- Reading the Unit Circle — the guide version of this table, explaining where the exact first-quadrant values come from.
- The Unit Circle: The One Idea Behind All of Trigonometry — how this same table underlies right-triangle ratios, the sine and cosine graphs, and the core identities.