Unit Circle Calculator: The Trigonometry Reference You Actually Need
The unit circle is a circle with radius 1, centered at the origin. For any angle θ, the coordinates of the point on the circle are (cos θ, sin θ). This single fact encodes all of trigonometry.
Key Angles and Their Values
| Angle | Degrees | sin | cos | tan |
|---|---|---|---|---|
| 0 | 0° | 0 | 1 | 0 |
| π/6 | 30° | 1/2 | √3/2 | 1/√3 |
| π/4 | 45° | √2/2 | √2/2 | 1 |
| π/3 | 60° | √3/2 | 1/2 | √3 |
| π/2 | 90° | 1 | 0 | undefined |
| π | 180° | 0 | -1 | 0 |
| 3π/2 | 270° | -1 | 0 | undefined |
| 2π | 360° | 0 | 1 | 0 |
The Memory Trick for 30-45-60
Sin values for 0°, 30°, 45°, 60°, 90°: √0/2, √1/2, √2/2, √3/2, √4/2
= 0, 1/2, √2/2, √3/2, 1
Cosine is sin in reverse: 1, √3/2, √2/2, 1/2, 0
Signs by Quadrant
The CAST rule (or "All Students Take Calculus"):
- Quadrant I (0–90°): All positive
- Quadrant II (90–180°): Sine positive
- Quadrant III (180–270°): Tangent positive
- Quadrant IV (270–360°): Cosine positive
Reference Angles
For any angle outside 0–90°, find the reference angle (acute angle to the x-axis), compute the trig value, then apply the correct sign for the quadrant.
sin(150°) = sin(30°) = 1/2 (Quadrant II, sine positive) ✓
cos(240°) = -cos(60°) = -1/2 (Quadrant III, cosine negative) ✓
[Use the unit circle calculator →](https://doesitaddup.com)
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