CVP verified calculation capability
cos(θ) in degrees (default) or radians, with algebraic snap for textbook angles.
Math Capability ID math.cos version 1.1.0 CVP VERIFIED CURRENT Core
Degrees
cos(θ°) = cos(θ × π/180)cos(θ)cos(θ) = adjacent / hypotenuseModes: angle · ratio · null
Canonical symbols for this capability. Agent schemas remain the contract.
| Symbol | Quantity | Unit | Role |
|---|---|---|---|
theta | scalar plane angle | — | input |
t | scalar plane angle | — | input |
angle | scalar plane angle | — | input |
thetaInput | scalar plane angle | — | input |
adjacent | — | — | input |
adjInput | — | — | input |
hypotenuse | — | — | input |
hypInput | — | — | input |
unit | — | — | input |
unitInput | — | — | input |
review | — | — | output |
api_version | — | — | output |
api_contract_version | — | — | output |
spec_version | — | — | output |
page | Canonical calculator page URL | — | output |
links | — | — | output |
Inspectable numeric contract for this Capability@Version. Not a rewrite of the engine.
| Field | Declaration |
|---|---|
numeric_domain | real |
exactness | float64 |
algorithm | Signed binary64 degree remainder and quadrant reduction before sin/cos; generic radians Math.cos; exact listed common degree identities and listed normalized binary64 radian tokens only, no angle-proximity epsilon; ratio mode adjacent/hypotenuse |
valid_domain | Angle mode: finite binary64 theta, deg(default)|rad; ratio mode: 0≤adjacent≤hypotenuse and hypotenuse>0. Strict decimal/scientific text≤512 chars; NUMERIC_UNDERFLOW for nonzero text→zero, RESULT_UNDERFLOW for nonzero ratio→zero; unknown/conflicting/inapplicable inputs reject. |
singularity_policy | not applicable — cosine has no real singularity; nearzero relative conditioning unbounded |
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 | 99 independent Decimal420/620 Taylor/Machin and Fraction fixed vectors;2ULP, strict zero/sign/types; legacy18 O3 vectors separately retain2ULP, not whole-domain guarantee |
golden_vectors | Evidence golden + boundary + property (and published_reference_case when listed) |
Declared scope for this capability. Do not use it outside this domain.
Assumptions
One numerical check. The calculator page holds worked steps and FAQ.
cos(60°) = 0.5; cos(π rad) = −1; cos(47.1°) ≈ 0.6807208689589178
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.
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 6/6.
curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/cos' \
-H 'Content-Type: application/json' \
-d '{"inputs":{"theta":60,"unit":"deg"},"calculation_version":"1.1.0"}'{
"inputs": {
"theta": 60,
"unit": "deg"
},
"calculation_version": "1.1.0"
}POST /api/v1/calc/cos. This is a POST calculate endpoint — do not GET it.
Full REST contract: REST API docs.
Declared calculation modes for this capability.
angleratioHuman-readable sources plus CVP reference evidence classes.
Sources
Derived identities
Reference evidence classes: O1 model · O3 expected_values · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
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.cos"},"_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.cos","inputs":{"theta":60,"unit":"deg"},"calculation_version":"1.1.0"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'Pin calculation_version (1.1.0) when the result must stay reproducible.
Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.