Trigonometric Identity Checker Calculator

Work out trigonometric identity checker instantly with clear inputs, formula shown and shareable results.

About Trigonometric Identity Checker Calculator

An identity holds for every admissible angle, so evaluating both sides numerically at a test angle is a quick sanity check. Agreement to within floating-point tolerance confirms the identity at that angle; genuine identities agree at every angle in their domain.

Formulas

Pythagorean identity

sin²θ + cos²θ = 1

Secant form

1 + tan²θ = sec²θ

Double angle

sin 2θ = 2 sin θ cos θ

Worked example

With the default values below, Trigonometric Identity Checker Calculator returns Verdict of Identity holds at this angle. Change any input above and every figure here is recalculated in your browser.

Inputs used

Test angle: 37 °
Identity to checkone of sin²θ + cos²θ = 1, tan θ = sin θ / cos θ, 1 + tan²θ = sec²θ, sin 2θ = 2 sin θ cos θ: sin²θ + cos²θ = 1

Results

Verdict: Identity holds at this angle
Left-hand side: 1.0000000000
Right-hand side: 1.0000000000
Absolute difference: 0.000000000000

Step by step

1Values used
2Pythagorean identity
3Secant form
4Double angle
5Verdict= Identity holds at this angle
6Left-hand side= 1.0000000000
7Right-hand side= 1.0000000000
8Absolute difference= 0.000000000000

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 12 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Does agreement at one angle prove an identity?

No. It only supports it. A proof requires algebra valid for all angles, though a single disagreement does disprove it.

Why do tiny differences appear?

Floating-point arithmetic rounds each operation, so exact identities can differ in the last few digits; a tolerance of 10⁻⁹ absorbs that.