Trig Identity Checker
Verify a trigonometric identity numerically by sampling angles and reporting max deviation.
Inputs
Verdict
VERIFIED — identity holds to machine precision
Max numerical deviation
2.2204 × 10⁻¹⁶
Worst-case angle
162.3800°
Identity
sin²θ + cos²θ = 1
Step by step
Identity tested
= sin²θ + cos²θ = 1
Angles sampled
= 100 angles across 0°–353°
Max deviation
= 2.2204e-16
Verdict
= Identity holds (deviation < 1e-10)
How it works
Rather than attempting a symbolic proof, this checker evaluates both sides of a trigonometric identity at 100 sample angles and reports the maximum numerical deviation. A deviation under 1×10⁻¹⁰ means the identity holds to floating-point precision.
Formulas
Pythagorean Identity
sin²θ + cos²θ = 1
- θ
- Any angle
Double Angle (sine)
sin(2θ) = 2·sin θ·cos θ
- θ
- Any angle
Frequently Asked Questions
Is numerical verification a real proof?
No — it is strong evidence but not a formal proof. However, for standard identities the deviation should be at floating-point error levels (< 10⁻¹⁴). A non-identity will show large deviation.
Why sample at irrational-step angles?
Using a non-round step avoids accidentally hitting only special angles where an identity might coincidentally hold but fail elsewhere.