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Trigonometric identities — one-page sheet
Tick the families you want on the page, then print or save as PDF. Nothing is uploaded; this is the same data the rest of the site is built from (44 identities, version 2026.09.26-1).
Special angles
| deg | rad | sin | cos | tan |
|---|---|---|---|---|
| 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 |
“undefined” marks where the function has no value (cos = 0 for tan, sin = 0 for cot/csc). Radians are exact multiples of π: π/12 = 15°.
Pythagorean identities
Reciprocal and quotient identities
Cofunction and even/odd identities
Sum and difference identities
Double-angle identities
Half-angle identities
Product-to-sum identities
Sum-to-product identities
Power-reducing identities
Triangle identities
trigidentity.com · every identity above was sampled at 800 angles by the same engine as trigidentity.com/verify · 2026-09-26 · half-angle roots need a sign chosen from the quadrant
Notes for whoever is teaching from this
- The two half-angle formulas print with ± because the square root needs a sign decided by the quadrant of x/2, not of x.
- Everything is Unicode text, so a browser's "Save as PDF" gives selectable text, not an image.
- Commercial or exam-question reuse: the data file is published at /data/identities.json under the terms on /terms.