CVP verified calculation capability

Tangent Calculation Capability

tan(θ) in degrees (default) or radians; exact odd multiples of 90° are UNDEFINED; near-pole returns finite with NEAR_SINGULARITY.

Math Capability ID math.tan version 1.0.4 CVP VERIFIED CURRENT Core

Model

Ratio

Ratio: tan(θ) = opposite / adjacent
Sin / cos: tan(θ) = sin(θ) / cos(θ)
Degrees: tan(θ°) = tan(θ × π/180)
Undefined when: cos(θ) = 0 (θ = 90° + 180°k)

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`theta`	Angle	—	input
`thetaInput`	Share-URL alias for theta	—	input
`unit`	Angle unit	—	input
`unitInput`	Share-URL alias for unit	—	input
`t`	—	—	input
`angle`	—	—	input
`api_version`	—	—	output
`api_contract_version`	—	—	output
`spec_version`	—	—	output
`page`	Canonical calculator page URL	—	output
`links`	—	—	output

Trusted Math contract

Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.

Field	Declaration
`numeric_domain`	real
`exactness`	float64
`algorithm`	float64 tan with algebraic snap; poles coded UNDEFINED
`valid_domain`	finite real angle not at π/2 + kπ (90° + k·180°)
`singularity_policy`	UNDEFINED when cos(θ) = 0 (odd multiples of 90°)
`branch_policy`	not applicable — real principal value only
`tolerance`	not applicable — closed form; capability Evidence owns comparison, no global default
`convergence`	not applicable — non-iterative
`conditioning`	not applicable — not a matrix κ product
`rounding`	ieee754_round_ties_to_even
`overflow`	ieee754_nonfinite_or_coded_error
`reproducibility`	deterministic algorithm + Capability@Version
`independent_oracle`	Evidence published cases
`golden_vectors`	Evidence golden + boundary + property (and published_reference_case when listed)

Assumptions / Validity

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

Assumptions

Real tangent only. Inverse is Arctan, not this published engine.
Documented pole classification: UNDEFINED when distance to 90° + 180°k is < 1e-12°. That threshold is a numerical classification policy, not a claim that those inputs are mathematically exact odd multiples of 90°. |cos(θ)| is not used as a pole test.
If the input is not classified as a pole and distance-to-pole < 0.01°, the engine returns a finite tan(θ) with warnings: [{ code: NEAR_SINGULARITY }]. status remains ok.
Documented common-angle snap: after reducing mod 360°, an input within 1e-12° of a listed common angle (0, ±30, ±45, ±60, …) is replaced by the algebraic value (0, ±1/√3, ±1, ±√3). This is a snap policy, not mathematical exactness. Nearby inputs such as 60.00000005° keep IEEE-754 Math.tan.
Documented cleanup: if no snap applies and |y| < 1e-12, the engine rewrites y to 0. That changes the IEEE-754 result for some non-zero inputs; it is a cleanup policy, not a mathematical identity.

Example

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

tan(45°) = 1 (listed snap); tan(90°) is classified UNDEFINED; tan(89.99999995°) is a large finite value with NEAR_SINGULARITY

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 (tan, invalid-domain, xcal)
Calculation version: 1.0.4
Verification: 25/25 calculation tests · 15/15 legacy golden · 10/10 legacy boundary
Production surface contract: 5/5
Versions: Calculation 1.0.4 · CVP protocol 1.0.0-proposed · Evidence 2026-09-08.policy
Verification revision: 2026-09-08.policy · 5/5 property · digest 494caf2c4f61
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: ≤2 ULP vs O3 applies to the 16 published tabulated vectors (common angles away from poles plus 8 seeded random angles in (−50°, 50°)). It is not a guarantee over the entire real line, including poles, 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 · 10/10 CVP boundary · 8/8 invalid · 5/5 property · 4/4 metamorphic · 4/4 round-trip · 16/16 O3 · 1/1 cross-interface · 11/11 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 · 1.0.4 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.0.4 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 5/5.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/tan' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"theta":45,"unit":"deg"},"calculation_version":"1.0.4"}'

{
  "inputs": {
    "theta": 45,
    "unit": "deg"
  },
  "calculation_version": "1.0.4"
}

POST /api/v1/calc/tan. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

Tool id: tan
Engine: tan
REST: POST /api/v1/calc/tan
MCP: execute_calculation with capability_id: "math.tan"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.4)
Versioned output schema: Immutable pin (1.0.4)

References

Human-readable sources plus CVP reference evidence classes.

Sources

Derived identities

CalculatorX mathematical conventions — Poles are UNDEFINED, not Infinity; inverse is Arctan

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

Try with an agent

Inspect, then execute. Same engine as REST and the human calculator.

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.tan"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

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: execute_calculation' \
  -d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"execute_calculation","arguments":{"capability_id":"math.tan","inputs":{"theta":45,"unit":"deg"},"calculation_version":"1.0.4"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

Pin calculation_version (1.0.4) when the result must stay reproducible.

Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.