Skip to content
cccskills
FreePublished on GitHub

trigonometric-functions

Abstract math for trigonometric functions: definitions, domains, ranges, key identities, and inverse functions. USE FOR: implementing sin/cos/tan/cot/sec/csc; implementing arcsin/arccos/arctan/atan2/acot/asec/acsc; validating input domains for inverse trig; applying Pythagorean and angle-sum identities; choosing atan vs atan2; precision near domain boundaries. DO NOT USE FOR: angle unit conversions (use angles-and-circular-arithmetic); coordinate system conversions (use coordinate-system-conversions); rotation representations (use 3d-rotation-theory).

The English summary is being prepared. Showing the original description.

NetFabric/NetFabric.Numerics36 stars(GitHub 36 + cccskills 0)

Run score Not tested

See how to install

Files included (3)

  • SKILL.md2.7 KB
  • references/formulas.md2.5 KB
  • references/numerical-stability.md2.3 KB

SKILL.md (original)

Review the instructions the agent will receive before you install.

Trigonometric Functions

Primary Functions

FunctionDefinitionDomainRange
sin θopposite / hypotenuseℝ[−1, 1]
cos θadjacent / hypotenuseℝ[−1, 1]
tan θsin θ / cos θℝ \ {π/2 + kπ}ℝ
cot θcos θ / sin θℝ \ {kπ}ℝ
sec θ1 / cos θℝ \ {π/2 + kπ}(−∞,−1] ∪ [1,∞)
csc θ1 / sin θℝ \ {kπ}(−∞,−1] ∪ [1,∞)

Inverse Functions

FunctionPrincipal RangeDomainNotes
arcsin x[−π/2, π/2][−1, 1]Odd function
arccos x[0, π][−1, 1]arccos = π/2 − arcsin
arctan x(−π/2, π/2)ℝOdd; atan(0) = 0
atan2(y,x)(−π, π]ℝ² \ {0,0}Signs of both args determine quadrant
acot x(0, π)ℝacot(x) = arctan(1/x) for x > 0
asec x[0,π] \ {π/2}|x| ≥ 1asec(x) = arccos(1/x)
acsc x[−π/2,π/2] \ {0}|x| ≥ 1acsc(x) = arcsin(1/x)

Key Identities

IdentityFormula
Pythagoreansin²θ + cos²θ = 1
Pythagorean (tan)1 + tan²θ = sec²θ
Pythagorean (cot)1 + cot²θ = csc²θ
Angle sum (sin)sin(α+β) = sin α cos β + cos α sin β
Angle sum (cos)cos(α+β) = cos α cos β − sin α sin β
Double angle (sin)sin(2θ) = 2 sin θ cos θ
Double angle (cos)cos(2θ) = cos²θ − sin²θ = 1 − 2sin²θ
Reflectionsin(π−θ) = sin θ; cos(π−θ) = −cos θ
Paritysin(−θ) = −sin θ (odd); cos(−θ) = cos θ (even)

atan2 vs atan

ScenarioUse
Need full 4-quadrant angle from (y, x)atan2(y, x)
x guaranteed positiveatan(y/x)
Computing angle between two vectorsatan2(cross, dot)

Reference Files

FileLoad When
references/formulas.mdFull identity table, reciprocal derivations, composition rules
references/numerical-stability.mdPrecision near ±1, atan2 singularities, cancellation in identities

Reviews

No reviews yet. Tell others what you thought.

Comments

No login needed. Share how it worked for you, ask a question, or note where it did not run.

No comments yet. Be the first to write one.

Comments are published right away. Do not include personal information such as email addresses or phone numbers. Up to 2 URLs.

0 / 1,000 characters

This form is protected by reCAPTCHA, and the Google Privacy Policy and Terms of Service apply.

More skills from this repository

Abstract math for 3D rotation representations and conversions. USE FOR: understanding axis-angle representation; Euler angles (yaw/pitch/roll, convention choices); rotation matrices (SO(3)); quaternion-based rotation; converting between representations; identifying and avoiding gimbal lock; composing rotations; half-angle formula; right-hand rule. DO NOT USE FOR: quaternion arithmetic details (use quaternion-algebra); slerp/lerp interpolation (use interpolation-on-manifolds); coordinate system definitions (use coordinate-system-conversions).

The English summary is being prepared. Showing the original description.

NetFabric/NetFabric.Numerics36Updated Aug 10, 2026

Design and scaffold multi-agent squads/swarms using the graph orchestration pattern (nodes = agents, edges = dependencies/data flow). USE FOR: designing a coordination topology for a multi-agent squad (sequential pipeline, parallel fan-out/aggregation, branching, feedback loop, cyclic); building an orchestrator agent that delegates to specialist agents; setting up an adversarial/tribunal code or document review with independent reviewers; scaffolding a squad's agent files for a target coding-agent harness (e.g. Copilot CLI or Claude Code custom agents). DO NOT USE FOR: authoring a single agent's frontmatter/prompt body (use copilot-cli-custom-agents, claude-code-custom-agents, or the target harness's own skill); SKILL.md authoring (use create-skill); ad-hoc multi-agent chat with no explicit topology.

The English summary is being prepared. Showing the original description.

NetFabric/NetFabric.Numerics36Updated Aug 10, 2026

Find, inspect, query, redact, and troubleshoot logs, transcripts, sessions, and OpenTelemetry data from coding-agent harnesses on Windows, macOS, Linux, and WSL. USE FOR: GitHub Copilot in VS Code; Copilot CLI; Claude Code; OpenAI Codex; Gemini CLI; OpenCode; Cursor, Windsurf, Kiro, or other VS Code-family editors; locating log files; diagnosing tool or model failures; correlating turns, subagents, and tool calls; querying JSONL, plaintext, or SQLite without spending model tokens; preparing sanitized diagnostics. DO NOT USE FOR: application logs unrelated to coding agents; uploading raw logs; treating unstable transcript schemas as public APIs.

The English summary is being prepared. Showing the original description.

NetFabric/NetFabric.Numerics36Updated Aug 10, 2026

Author and maintain AGENTS.md files — the open, tool-agnostic format for giving coding agents project context. Use when: creating AGENTS.md; writing an agent instructions file; root or nested AGENTS.md for monorepos; migrating CLAUDE.md, AGENT.md, .cursor/rules, or copilot-instructions.md to AGENTS.md; greenfield project setup before code exists; brownfield onboarding for an existing codebase; documenting build/test/lint commands, code style, PR/commit conventions, and security considerations for agents; AGENTS.md discovery and precedence rules. Works for any language, framework, or project size. DO NOT USE FOR: authoring SKILL.md skill files (use create-skill); APM package/plugin authoring (use apm-producer); language-specific style rules (use language skills e.g. csharp-best-practices).

The English summary is being prepared. Showing the original description.

NetFabric/NetFabric.Numerics36Updated Aug 10, 2026

Abstract math for angle measurement, unit systems, and circular arithmetic. USE FOR: implementing angle types; converting between degrees/radians/gradians/revolutions; reducing angles to canonical range [0, Full); computing reference angles and quadrants; implementing safe modular arithmetic with negative inputs; angle addition and subtraction; classifying angles by sign and size. DO NOT USE FOR: trigonometric functions (use trigonometric-functions); coordinate conversions (use coordinate-system-conversions); interpolation (use interpolation-on-manifolds).

The English summary is being prepared. Showing the original description.

NetFabric/NetFabric.Numerics36Updated Aug 10, 2026

Create and maintain Claude Code custom subagents (.claude/agents/*.md files). USE FOR: authoring project (.claude/agents/) or user (~/.claude/agents/) subagent files; frontmatter fields (name, description, tools, disallowedTools, model, permissionMode, maxTurns, skills, mcpServers, hooks, memory, background, effort, isolation, color, initialPrompt); writing descriptions that drive automatic delegation and 'use proactively' phrasing; invoking subagents via natural language, @-mention, session-wide --agent, or the Agent tool; restricting which subagent types a coordinator can spawn with Agent(name1, name2); nested subagents and depth limits; built-in subagents (Explore, Plan, general-purpose, claude); troubleshooting a subagent that won't load or isn't invoked. DO NOT USE FOR: GitHub Copilot CLI custom agents (use copilot-cli-custom-agents); agent teams/teammates (a different, session-spanning feature); MCP server authoring; SKILL.md authoring (use create-skill).

The English summary is being prepared. Showing the original description.

NetFabric/NetFabric.Numerics36Updated Aug 10, 2026

See all skills by NetFabric

Report a problem with this skill