Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add hamzabellouch/agent-skills --skill trigonometry-and-geometrygit clone --depth 1 https://github.com/hamzabellouch/agent-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/hamzabellouch/agent-skills/trigonometry-and-geometry)<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/trigonometry-and-geometry"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/trigonometry-and-geometry/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/trigonometry-and-geometry"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/trigonometry-and-geometry.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00062 | $0.00751 |
| Opus 5.5 | $0.00025 | $0.00300 |
| Sonnet 5.5 | $0.00012 | $0.00150 |
| Haiku 4.5 | $0.00006 | $0.00075 |
Grade A, and why
trigonometry-and-geometry scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured today.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
What it actually says
Geometry & Trigonometry
Plane geometry
- Triangle: angle sum 180; area = 1/2 bh = 1/2 ab sinC = sqrt(s(s-a)(s-b)(s-c)) (Heron); inradius r = Area/s; circumradius R = abc/(4 Area).
- Pythagoras a^2 + b^2 = c^2; special triangles 30-60-90 (1, sqrt3, 2), 45-45-90.
- Similarity: AA, SAS, SSS; area ratio = (scale)^2. Congruence: SSS, SAS, ASA, AAS, HL.
- Centers: centroid (2:1 on medians), incenter, circumcenter, orthocenter; Euler line.
- Circle: C = 2 pi r, A = pi r^2; inscribed angle = 1/2 central angle; tangent perpendicular to radius; power of a point; chords: ab = cd.
- Polygons: interior angle sum (n-2)180; regular n-gon area = 1/2 (perimeter)(apothem).
- Theorems: Angle bisector, Menelaus, Ceva, Ptolemy (cyclic quadrilateral ac + bd = pq), Stewart.
Solid geometry
Sphere V = 4/3 pi r^3, S = 4 pi r^2; cone V = 1/3 pi r^2 h; cylinder V = pi r^2 h; pyramid V = 1/3 Bh; Euler V - E + F = 2.
Coordinate geometry
Distance, midpoint, slope, line equations (point-slope), circle (x-h)^2 + (y-k)^2 = r^2, conics: ellipse x^2/a^2 + y^2/b^2 = 1, parabola, hyperbola; shoelace formula for polygon area.
Trigonometry
- Definitions SOH-CAH-TOA; unit circle; radians: 180 deg = pi rad.
- Identities: sin^2 + cos^2 = 1; sin(a+b) = sin a cos b + cos a sin b; cos(a+b) = cos a cos b - sin a sin b; double angle sin 2a = 2 sin a cos a, cos 2a = cos^2 a - sin^2 a; sum-to-product; tan = sin/cos.
- Law of sines a/sinA = 2R; law of cosines c^2 = a^2 + b^2 - 2ab cosC. Ambiguous case SSA may give 0, 1, or 2 triangles.
- Graphs: amplitude, period 2 pi/b, phase shift; inverse trig ranges (arcsin [-pi/2, pi/2], arccos [0, pi], arctan (-pi/2, pi/2)).
- Euler: e^(i theta) = cos theta + i sin theta; De Moivre.
Method
Draw an accurate diagram, label knowns, look for right triangles / similar triangles / cyclic quadrilaterals, try coordinates or complex numbers when synthetic proof stalls.
What ships with it
1 file beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- today First seen · 32 lines · 62 tokens per session scan A 89446646e019
trigonometry-and-geometry is a skill published in the GitHub repository hamzabellouch/agent-skills (8 stars, last pushed today), licensed MIT. It adds 62 tokens to every session and 751 once invoked, about $0.0002 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-10-17.
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