The trick to remember the first table
Write 0, 1, 2, 3, 4. Divide each by 4 and take the square root. That gives 0, 1/2, 1/√2, √3/2 and 1, which are sin 0°, 30°, 45°, 60° and 90°. Cos is the same row backwards, and tan is sin ÷ cos.
Signs in each quadrant: All Students Take Coffee
- Quadrant I (0°–90°): all ratios are positive.
- Quadrant II (90°–180°): only sin and cosec.
- Quadrant III (180°–270°): only tan and cot.
- Quadrant IV (270°–360°): only cos and sec.
For sin 150°, write it as sin(180° − 30°). It's in quadrant II, where sin is positive, so sin 150° = sin 30° = 1/2.
Every 5°, to four decimals
| θ | sin θ | cos θ | tan θ |
|---|---|---|---|
| 0° | 0.0000 | 1.0000 | 0.0000 |
| 5° | 0.0872 | 0.9962 | 0.0875 |
| 10° | 0.1736 | 0.9848 | 0.1763 |
| 15° | 0.2588 | 0.9659 | 0.2679 |
| 20° | 0.3420 | 0.9397 | 0.3640 |
| 25° | 0.4226 | 0.9063 | 0.4663 |
| 30° | 0.5000 | 0.8660 | 0.5774 |
| 35° | 0.5736 | 0.8192 | 0.7002 |
| 40° | 0.6428 | 0.7660 | 0.8391 |
| 45° | 0.7071 | 0.7071 | 1.0000 |
| 50° | 0.7660 | 0.6428 | 1.1918 |
| 55° | 0.8192 | 0.5736 | 1.4281 |
| 60° | 0.8660 | 0.5000 | 1.7321 |
| 65° | 0.9063 | 0.4226 | 2.1445 |
| 70° | 0.9397 | 0.3420 | 2.7475 |
| 75° | 0.9659 | 0.2588 | 3.7321 |
| 80° | 0.9848 | 0.1736 | 5.6713 |
| 85° | 0.9962 | 0.0872 | 11.4301 |
| 90° | 1.0000 | 0.0000 | Not defined |
All the identities are on the maths formula sheet.
Exact values of special angles
Tap a value for its derivation.
Questions students ask
What is the value of sin 30°?
1/2. Cos 60° is also 1/2.
What is tan 90°?
Not defined, because cos 90° = 0 and tan is sin ÷ cos. Cot 90° is 0.
What is cos 120°?
−1/2. Write it as cos(180° − 60°). Cos is negative in quadrant II, so cos 120° = −cos 60° = −1/2.
How do I remember the trigonometry table?
For sin at 0°, 30°, 45°, 60° and 90°, take √(n/4) for n = 0 to 4. Cos is the same list reversed, and tan is sin divided by cos.