Geometry and trigonometry
Use coordinates, similarity, area, volume and angle ratios to construct and check a geometric design with explicit units and domains.
Choose any lesson or try the project first. Shared lessons retain the same saved work wherever you enter them. Completing a lesson records participation; practice, transfer checks and independent reasoning remain separate.
Recommended preparation and ways to catch up
- Multiply fractions and squared quantities.
- Read signed coordinates; the existing coordinate lesson is included as a direct entry.
- No calculus is needed before the optional local-motion extension.
Find a foundation course · Open contextual refreshers. Each investigation includes a short recap; preparation never locks access.
Loading local course progress…
Your units and lessons
Choose a unit to see its lesson sequence. Every lesson opens on its own page.
Locate and measure
Read coordinates, compute straight distances and distinguish direction ratios from lengths.
Read a graph with its units
Connect a table, a coordinate pair and a point without being misled by axis scales.
A route, a distance and a slope are different
How do coordinates determine distance without confusing it with direction?
Scale a design
Preserve shape while correctly scaling perimeter, area and volume.
Scaling length does not scale everything equally
What happens to area and volume when every length doubles?
Turn angles into positions
Use signed sine and cosine, convert angle units, and inspect a local-motion extension with stated derivative assumptions.
Turn an angle into two coordinates
Why can sine or cosine be negative when a triangle side length cannot?
Turn an angle into local motion
Connect trigonometry, rotations, Jacobians, least-squares motion and singularities.
Design a scaled layout and an angled reach
Create a geometric design for a model display, storage layout or virtual reach mechanism. Specify coordinates, a uniform scale and an angled segment. Verify its dimensions, area or volume, and endpoint independently. Use at least two investigation mechanisms; a plausible drawing alone is insufficient.
Build from lesson evidence, compare alternatives, write an artifact, and tackle unfamiliar numerical cases. Use the rubric with a teacher, peer or colleague to assess the quality of your reasoning.
Open the course project