Trigonometric Values Table (0° to 360° Standard Angles)
This trigonometry table lists sin, cos, tan, cosec, sec and cot for the standard angles from 0 to 360 degrees, with radians, exact values and quadrant signs, plus a calculator for any angle.
sin 30°1/2Equal to cos 60°
sin 45° = cos 45°√2 / 2About 0.7071
sin 60°√3 / 2Equal to cos 30°, about 0.8660
tan 45°1sin and cos are equal at 45°
Degrees to Radians180° = π radMultiply degrees by π / 180
Signs (ASTC)All, Sin, Tan, CosPositive in Quadrants I, II, III, IV
Trig Values Calculator
Tip: open this page with ?angle=45 (degrees, 0 to 360) to start with that angle and highlight its row. Standard angles also show exact values such as √3/2.
| Angle (Deg) | Radians | sin | cos | tan | cosec | sec | cot | Copy |
|---|---|---|---|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 | undefined | 1 | undefined | |
| 30° | π/6 | 1/2 | √3/2 | √3/3 | 2 | 2√3/3 | √3 | |
| 45° | π/4 | √2/2 | √2/2 | 1 | √2 | √2 | 1 | |
| 60° | π/3 | √3/2 | 1/2 | √3 | 2√3/3 | 2 | √3/3 | |
| 90° | π/2 | 1 | 0 | undefined | 1 | undefined | 0 | |
| 120° | 2π/3 | √3/2 | −1/2 | −√3 | 2√3/3 | −2 | −√3/3 | |
| 135° | 3π/4 | √2/2 | −√2/2 | −1 | √2 | −√2 | −1 | |
| 150° | 5π/6 | 1/2 | −√3/2 | −√3/3 | 2 | −2√3/3 | −√3 | |
| 180° | π | 0 | −1 | 0 | undefined | −1 | undefined | |
| 210° | 7π/6 | −1/2 | −√3/2 | √3/3 | −2 | −2√3/3 | √3 | |
| 225° | 5π/4 | −√2/2 | −√2/2 | 1 | −√2 | −√2 | 1 | |
| 240° | 4π/3 | −√3/2 | −1/2 | √3 | −2√3/3 | −2 | √3/3 | |
| 270° | 3π/2 | −1 | 0 | undefined | −1 | undefined | 0 | |
| 300° | 5π/3 | −√3/2 | 1/2 | −√3 | −2√3/3 | 2 | −√3/3 | |
| 315° | 7π/4 | −√2/2 | √2/2 | −1 | −√2 | √2 | −1 | |
| 330° | 11π/6 | −1/2 | √3/2 | −√3/3 | −2 | 2√3/3 | −√3 | |
| 360° | 2π | 0 | 1 | 0 | undefined | 1 | undefined |
| Angle (Deg) | Radians | sin | cos | tan | cosec | sec | cot | Copy |
|---|---|---|---|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 | undefined | 1 | undefined | |
| 30° | 0.5236 | 0.5 | 0.866 | 0.5774 | 2 | 1.1547 | 1.7321 | |
| 45° | 0.7854 | 0.7071 | 0.7071 | 1 | 1.4142 | 1.4142 | 1 | |
| 60° | 1.0472 | 0.866 | 0.5 | 1.7321 | 1.1547 | 2 | 0.5774 | |
| 90° | 1.5708 | 1 | 0 | undefined | 1 | undefined | 0 | |
| 120° | 2.0944 | 0.866 | -0.5 | -1.7321 | 1.1547 | -2 | -0.5774 | |
| 135° | 2.3562 | 0.7071 | -0.7071 | -1 | 1.4142 | -1.4142 | -1 | |
| 150° | 2.618 | 0.5 | -0.866 | -0.5774 | 2 | -1.1547 | -1.7321 | |
| 180° | 3.1416 | 0 | -1 | 0 | undefined | -1 | undefined | |
| 210° | 3.6652 | -0.5 | -0.866 | 0.5774 | -2 | -1.1547 | 1.7321 | |
| 225° | 3.927 | -0.7071 | -0.7071 | 1 | -1.4142 | -1.4142 | 1 | |
| 240° | 4.1888 | -0.866 | -0.5 | 1.7321 | -1.1547 | -2 | 0.5774 | |
| 270° | 4.7124 | -1 | 0 | undefined | -1 | undefined | 0 | |
| 300° | 5.236 | -0.866 | 0.5 | -1.7321 | -1.1547 | 2 | -0.5774 | |
| 315° | 5.4978 | -0.7071 | 0.7071 | -1 | -1.4142 | 1.4142 | -1 | |
| 330° | 5.7596 | -0.5 | 0.866 | -0.5774 | -2 | 1.1547 | -1.7321 | |
| 360° | 6.2832 | 0 | 1 | 0 | undefined | 1 | undefined |
| Quadrant | Angle Range | Reference Angle | Positive | Negative | Copy |
|---|---|---|---|---|---|
| Quadrant I | 0° to 90° | θ | All six (sin, cos, tan, cosec, sec, cot) | None | |
| Quadrant II | 90° to 180° | 180° − θ | sin, cosec | cos, sec, tan, cot | |
| Quadrant III | 180° to 270° | θ − 180° | tan, cot | sin, cosec, cos, sec | |
| Quadrant IV | 270° to 360° | 360° − θ | cos, sec | sin, cosec, tan, cot |
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Frequently Asked Questions
| Question | Answer |
|---|---|
| What are the trigonometric values for 0, 30, 45, 60 and 90 degrees? | sin: 0, 1/2, √2/2, √3/2, 1. cos: 1, √3/2, √2/2, 1/2, 0. tan: 0, √3/3, 1, √3, undefined. |
| How do you convert degrees to radians? | Multiply the degrees by π/180. So 180 degrees = π, 90 degrees = π/2, 30 degrees = π/6 and a full turn of 360 degrees = 2×π radians. |
| How do you find trig values for angles above 90 degrees? | Find the reference angle (the acute angle to the x-axis), take its value, and apply the sign of the quadrant. For 150 degrees the reference angle is 30 degrees, so sin 150 = sin 30 = 1/2 and cos 150 = −cos 30 = −√3/2. |
| What does ASTC (All Students Take Calculus) mean? | It lists which functions are positive in each quadrant: All in Quadrant I, Sine (and cosec) in II, Tangent (and cot) in III, and Cosine (and sec) in IV. |
| Why are tan 90 and tan 270 undefined? | At 90 and 270 degrees cos = 0, and tan = sin / cos would divide by zero. For the same reason sec is undefined there, and cosec and cot are undefined at 0, 180 and 360 degrees where sin = 0. |
| What are sin, cos and tan of 180 and 360 degrees? | At 180 degrees: sin = 0, cos = −1, tan = 0. At 360 degrees: sin = 0, cos = 1, tan = 0. |