Trigonometric Functions
SkillMonitoring & opsAbstract 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).
Available today. Use it from your connected AI after setup.
No other account needed.
Connect ahel once, and every AI you use reads what you have installed.
Then ask your AI: use the Trigonometric Functions skill
What this skill tells your AI
The instructions your AI receives, as published by netfabric/netfabric.numerics in .agents/skills/trigonometric-functions/SKILL.md and read by ahel’s review.
Primary Functions
| Function | Definition | Domain | Range |
|---|---|---|---|
| sin θ | opposite / hypotenuse | ℝ | [−1, 1] |
| cos θ | adjacent / hypotenuse | ℝ | [−1, 1] |
| tan θ | sin θ / cos θ | ℝ \ {π/2 + kπ} | ℝ |
| cot θ | cos θ / sin θ | ℝ \ {kπ} | ℝ |
| sec θ | 1 / cos θ | ℝ \ {π/2 + kπ} | (−∞,−1] ∪ [1,∞) |
| csc θ | 1 / sin θ | ℝ \ {kπ} | (−∞,−1] ∪ [1,∞) |
Inverse Functions
| Function | Principal Range | Domain | Notes |
|---|---|---|---|
| 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) | ℝ | Odd; atan(0) = 0 |
| atan2(y,x) | (−π, π] | ℝ² \ {0,0} | Signs of both args determine quadrant |
| acot x | (0, π) | ℝ | acot(x) = arctan(1/x) for x > 0 |
| asec x | [0,π] \ {π/2} | |x| ≥ 1 | asec(x) = arccos(1/x) |
| acsc x | [−π/2,π/2] \ {0} | |x| ≥ 1 | acsc(x) = arcsin(1/x) |
Key Identities
| Identity | Formula |
|---|---|
| Pythagorean | sin²θ + 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 |
| Reflection | sin(π−θ) = sin θ; cos(π−θ) = −cos θ |
| Parity | sin(−θ) = −sin θ (odd); cos(−θ) = cos θ (even) |
atan2 vs atan
| Scenario | Use |
|---|---|
| Need full 4-quadrant angle from (y, x) | atan2(y, x) |
| x guaranteed positive | atan(y/x) |
| Computing angle between two vectors | atan2(cross, dot) |
Reference Files
| File | Load When |
|---|---|
| references/formulas.md | Full identity table, reciprocal derivations, composition rules |
| references/numerical-stability.md | Precision near ±1, atan2 singularities, cancellation in identities |
Signals
- GitHub stars
- 36
- Forks
- 1
- Last commit
- Aug 2026
Advanced
- Catalog kind
- skill
- Gateway key
trigonometric-functions- Source
- github.com/netfabric/netfabric.numerics