Sine-Curve Tangent-Projection Locus Explorer

Sine curveMoving BTangent at BFixed CProjection DLocus of D

Geometry and motion

Frequency a

Fixed point C: x

Fixed point C: y

Moving parameter x

Swing speed

Locus resolution

The domain is fixed: x ∈ [−π,+π]. The swing uses a reflected linear parameter, so B moves from −π to +π, reverses, and returns without wrapping around.

Current quantities

Moving point B—

Projection D—

Tangent slope—

Projection distance CD—

Locus x range—

Curve: y = sin(ax)

At B = (u, sin(au)), tangent slope:
m = a cos(au)

Tangent: y − sin(au) = m(x − u)

For C = (cₓ,cᵧ), let b = sin(au) − mu.
The perpendicular foot is:
D = C + q(−m,1),
q = (m cₓ − cᵧ + b)/(m²+1).

Animation domain: u ∈ [−π,+π].