Trig Identity Evaluator

Formula

How this is calculated

You choose an identity from the menu — the Pythagorean identity (sin²θ + cos²θ = 1), the tangent quotient (tan θ = sin θ / cos θ), the double-angle forms (sin 2θ = 2 sin θ cos θ and cos 2θ = cos²θ − sin²θ), or the half-angle form (sin²(θ/2) = (1 − cos θ)/2). You then enter an angle θ and select whether it is given in degrees or radians.

The calculator first converts θ to radians (multiplying degrees by π/180), because JavaScript trigonometric functions operate in radians. It then evaluates the left-hand side (LHS) and the right-hand side (RHS) of the identity independently using Math.sin, Math.cos, and Math.tan, and reports the absolute difference |LHS − RHS|. Because these are universal identities, that difference should be zero for every valid angle; in practice it is a tiny floating-point residual on the order of 1e-16, so the identity is flagged as verified whenever the difference is below the 1e-9 tolerance.

Watch for angles where a function is undefined: tan θ and the tangent quotient blow up near θ = 90° (π/2) because cos θ approaches zero, producing very large values and large floating-point error. Otherwise the residual stays negligible. The result is dimensionless — all outputs are pure ratios — and the tool is meant to demonstrate that these identities hold, not to solve for an unknown angle.