Verified calculation capability

Sine Calculation Capability

sin(θ) in degrees (default) or radians, with algebraic snap for textbook angles. · Math

Capability ID math.sin · version 1.0.5

Open calculator REST API MCP Evidence Evidence JSON CVP Manifest Review policy

Model

Degrees

Degrees: sin(θ°) = sin(θ × π/180)
Radians: sin(θ)
Triangle: sin(θ) = opposite / hypotenuse
Unit circle: sin(θ) = y-coordinate

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`theta`	Angle. Aliases: t, angle, thetaInput	—	input
`thetaInput`	Share-URL alias for theta	—	input
`unit`	Angle unit (default deg)	—	input
`unitInput`	Share-URL alias for unit	—	input
`t`	time	—	input
`angle`	—	—	input
`formula`	—	—	output
`api_version`	—	—	output
`api_contract_version`	—	—	output
`spec_version`	—	—	output
`page`	Canonical calculator page URL	—	output
`links`	—	—	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

Assumptions

Real sine. The published engine is forward sin(θ). Opposite/hypotenuse is a local triangle convenience (hypotenuse > 0, opposite ≥ 0, opposite ≤ hypotenuse). Use Arcsin for the inverse API.
Algebraic snap applies only when the reduced angle (mod 360°) is a listed identity such as 0°, 30°, 45°, 60°, 90°. Nearby floats, including 30.00000005°, keep IEEE-754 Math.sin.

Example

One numerical check. The calculator page holds worked steps and FAQ.

sin(30°) = 0.5; sin(π/6 rad) = 0.5; sin(47.1°) ≈ 0.7325428987873787

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance· View Manifest · CVP overview · Specification
Assurance: Core
Declared partition coverage: PASS · 3/3 declared partitions (sin, invalid-domain, xcal)
Calculation version: 1.0.5
Verification: 11/11 calculation tests · 7/7 legacy golden · 4/4 legacy boundary
Production surface contract: 3/3
Versions: Calculation 1.0.5 · CVP protocol 1.0.0-proposed · Evidence 2026-09-08.xcal
Verification revision: 2026-09-08.xcal · 3/3 property · digest f6d938207118
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: ≤2 ULP vs O3 applies to the 18 published tabulated vectors (common angles 0°…180° plus 8 seeded random angles in (−50°, 50°)). It is not a guarantee over the entire real line, including huge angles or unlisted neighborhoods of zeros.
Interfaces: PASS · UI (SSR) / REST / MCP / URL→result→graph
Success 1/1. Integration: URL → SSR result → Live graph current point (4/4). Hydration/slider/history are URL-canonical contracts, not a live browser session.
CVP suite: 4/4 golden · 4/4 CVP boundary · 4/4 invalid · 3/3 property · 3/3 metamorphic · 4/4 round-trip · 18/18 O3 · 1/1 cross-interface · 8/8 cross-calculator · 4/4 URL→result→graph · 1/1 CVP contract
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.5 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.0.5 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 3/3.

Tool id: sin
Engine: sin
REST: POST /api/v1/calc/sin
MCP: execute_calculation with capability_id: "math.sin"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.5)
Versioned output schema: Immutable pin (1.0.5)

References

Human-readable sources plus CVP reference evidence classes.

Sources

NIST Digital Library of Mathematical Functions, Chapter 4 — Elementary Functions
NIST DLMF §4.14 — Definitions and period of sine and cosine
CalculatorX mathematical conventions — Degree default; listed-identity exact values; inverse is Arcsin

Reference evidence classes: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior

Try with an agent

Inspect this capability via same-origin MCP, then call execute_calculation.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"math.sin"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.0.5) when reproducibility matters. Full protocol notes: MCP docs.