Trig Function & Identity Calculator
Evaluate sine, cosine, tangent, cosecant, secant, and cotangent at any angle in degrees or radians — with undefined values handled cleanly and the Pythagorean identity checked live.
The six trigonometric functions
Pythagorean identity check: sin²θ + cos²θ = 1 (always 1).
All six functions, plus a sanity check
The three reciprocal functions — cosecant, secant, and cotangent — trip up a lot of students simply because they are easy to mix up. Seeing all six values side by side for the same angle makes the reciprocal relationships concrete: cosecant mirrors sine, secant mirrors cosine, and cotangent mirrors tangent.
The tool also displays sin²θ + cos²θ, the Pythagorean identity, which stays equal to 1 for every angle you enter. It’s a small, reassuring reminder that the identities you memorise really are always true.
Frequently Asked Questions
What are the six trigonometric functions?
Sine, cosine, and tangent are the three primary ratios; cosecant, secant, and cotangent are their reciprocals. Cosecant is 1 / sine, secant is 1 / cosine, and cotangent is 1 / tangent (equivalently cosine / sine). Entering one angle gives you all six at once.
Why does the tool sometimes say a value is undefined?
A reciprocal function is undefined wherever its denominator is zero. Tangent and secant are undefined at 90° and 270°, where cosine is zero; cosecant and cotangent are undefined at 0° and 180°, where sine is zero. Rather than show a divide-by-zero result, the calculator marks those cells as undefined.
What does the Pythagorean identity check show?
The identity sin²θ + cos²θ = 1 holds for every angle. The tool computes sin²θ + cos²θ from your angle and displays it, which should always come out to 1. It's a quick way to see the most important trig identity holding true no matter which angle you try.
Can I enter the angle in radians?
Yes. Switch the unit selector to radians and enter the angle directly — π/2, 1.0472, or any value. The calculator evaluates the functions the same way; only the interpretation of the input number changes between degrees and radians.
Educational tool only. Values are rounded for display; use full precision where an application requires it.