Trig / Unit Circle Calculator
Calculate sin, cos, tan, csc, sec, and cot for any angle, while showing the quadrant, reference angle, and exact values for standard unit-circle angles.
Last updated: 2026-03-25
Trig / unit circle calculator
Enter your values
Enter any angle in degrees or radians and return the main trig ratios plus unit-circle context.
sin / cos / tan
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Enter an angle in degrees or radians to calculate the six trig ratios and see the unit-circle context.
Calculation History(0)
Example calculations
Tap an example to prefill the calculator with sample values.
Standard angle
135 degrees in Quadrant II
A standard unit-circle angle that also produces exact values.
Result: The calculator returns exact unit-circle values and the reference angle.
Negative radian input
-5pi/6 approximated in radians
Useful when you need normalization back into the 0 to 360 degree range.
Result: The tool normalizes the angle and still returns the correct quadrant and trig outputs.
How the trig calculator works
The calculator converts the input to degrees, normalizes it onto the unit circle, and then evaluates sine and cosine at that position. Tangent, secant, cosecant, and cotangent are derived from those core values.
For standard angles, the output also surfaces the familiar exact-value identities used in algebra and precalculus classes.
Trig calculator FAQs
Use these answers to interpret normalized angles, exact values, and undefined tangent or secant cases.
Why normalize the angle first?
Angles that differ by full rotations land at the same point on the unit circle. Normalizing puts the angle into a familiar 0 to 360 degree range while preserving the trig values.
When do exact values appear?
Exact radical values appear for common unit-circle angles like 30, 45, 60, 120, 135, and 150 degrees. For arbitrary angles, the calculator returns decimal approximations.
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