This trigonometry calculator normalizes any angle and reports unit-circle coordinates, quadrant, and exact values for special angles.
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Unit Circle Calculator
Normalize any angle and calculate its unit-circle coordinates and exact special-angle values.
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About this calculator
Formula notes
Normalize the angle to 0-360 degrees, then compute sine, cosine, and tangent with standard trigonometric functions; special angles also receive exact radical forms.
Worked examples
- Example: 45 degrees gives sine and cosine sqrt(2)/2, tangent 1, and quadrant I.
- At 90 degrees, cosine is 0, so tangent is undefined while sine is 1.
How to use it
- Enter an angle in degrees, radians, x pi radians, or turns.
- Read the normalized angle and quadrant.
- Check sine, cosine, tangent, and exact special-angle values.
Frequently asked questions
Why is tangent undefined for some angles?
At 90 and 270 degrees cosine is zero, so tangent has no finite value; the tool reports it as undefined.
Are exact values available for every angle?
No. Exact labels are provided for common special angles; other angles use numeric trigonometric results.
Limits and interpretation
- Trigonometric outputs use JavaScript double-precision math; tiny floating-point residuals can appear near special angles.
- Exact radical labels are available only for recognized special angles; other angles show numeric values.