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Track recap

Track recap140 min

Complex and Parametric Motion

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Start with complex numbers as points on one plane, turn that plane into unit-circle and polar-coordinate geometry, deepen that same bench into trig identities and inverse-angle reasoning, then carry the coordinate language into motion traced from x(t) and y(t).

About recap mode

Keep the authored order, then open the extra explanation only when you need to understand how recap is choosing the next review move.

How it works

Same authored sequence, lighter revisit.

Recap mode does not invent a second curriculum. It keeps the existing starter-track order, then changes the prompt and suggested action with the current mastery and progress signals.

Keep using concept pages

Quick tests, challenge mode, worked examples, and read-next stay where they already live.

Recap links only jump you to the most useful surface for a fast review. The simulation-first concept pages still carry the real teaching work and keep the guided path intact.

Recap steps

Revisit the track in the same authored order.

Focus badges and button targets come from the current mastery and progress signals. The next ready checkpoint still stays in the loop.

  1. 1Not startedNewNext guided step

    Complex Numbers on the Plane

    Complex Numbers on the Plane is still the next guided step in this authored order. No finished quick test, solved challenge, or completion mark is saved yet.

    Start here before moving into Unit Circle / Sine and Cosine from Rotation.

    Real and imaginary partsMagnitude and argument25 min
  2. 2Not startedNewAhead

    Unit Circle / Sine and Cosine from Rotation

    This concept stays in the recap because it completes the authored track story, even if you have not reached it on this browser yet.

    Builds on Complex Numbers on the Plane before setting up Polar Coordinates / Radius and Angle.

    cosine as xsine as y20 min
  3. 3Not startedNewAhead

    Polar Coordinates / Radius and Angle

    This concept stays in the recap because it completes the authored track story, even if you have not reached it on this browser yet.

    Builds on Unit Circle / Sine and Cosine from Rotation before setting up Trig Identities from Unit-Circle Geometry.

    Radius and angle on one planex = r cos(theta)22 min
  4. 4Not startedNewAhead

    Trig Identities from Unit-Circle Geometry

    This concept stays in the recap because it completes the authored track story, even if you have not reached it on this browser yet.

    Builds on Polar Coordinates / Radius and Angle before setting up Inverse Trig / Angle from Ratio.

    cos^2 + sin^2 = 1Complementary-angle swap24 min
  5. 5Not startedNewAhead

    Inverse Trig / Angle from Ratio

    This concept stays in the recap because it completes the authored track story, even if you have not reached it on this browser yet.

    Builds on Trig Identities from Unit-Circle Geometry before setting up Parametric Curves / Motion from Equations.

    tan(theta) as y/xPrincipal-angle output24 min
  6. 6Not startedNewAhead

    Parametric Curves / Motion from Equations

    This concept stays in the recap because it completes the authored track story, even if you have not reached it on this browser yet.

    Capstone step after Inverse Trig / Angle from Ratio.

    x(t) and y(t) togetherPath vs traversal25 min