Unit Circle Calculator
Unit circle calculator works out Result and Result unit from Angle. The default figures on this page give result of 0.707106781; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
3 steps
- θ = 45 deg = 0.7853981634 rad (× π/180 for degrees)
- sin(45°) = 0.7071067812
- Coterminal angle in [0°, 360°) = 45°, quadrant I, reference angle 45°
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
3 sources
What the unit circle calculator calculates
Evaluates sine, cosine, tangent, their reciprocals and hyperbolic partners, or inverts any of them, and reports all six circular functions of the resulting angle with its quadrant, reference angle and exact unit-circle value.
How to use this unit circle calculator
Enter Angle. Result updates as you type. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Result, Result unit and Angle.
The method follows NIST Digital Library of Mathematical Functions, Chapter 4: Elementary Functions (trigonometric and inverse trigonometric), Weisstein, Eric W. "Inverse Cotangent." MathWorld — principal branch (0, π) convention and Abramowitz & Stegun, Handbook of Mathematical Functions, Chapter 4.
What you can compare
Change one input at a time to see how it affects Result, Result unit and Angle. The inputs you can vary are Angle.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
What information do I need for the unit circle calculator?
You need Angle. The page opens with default figures that give result of 0.707106781, so you can see the scale before entering your own.
What does this unit circle calculator show?
It shows Result, Result unit, Angle, sin θ, cos θ, tan θ, csc θ and sec θ, with the working and any warnings for your entries.
Can I check how the unit circle calculator result was calculated?
Yes. The “How this is worked out” section shows the calculation steps, and the sources section identifies the references used for the method.