Source: https://guthlabs.ai/docs/instruments/unit-circle-explorer/mechanism/

instrument mechanism / verified-clean

# Unit Circle Explorer mechanism

The inspectable method record for Unit Circle Explorer, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The core unit-circle coordinate formula is standard and correct. The specification needs explicit angle-unit behavior, normalization, reference-angle convention, tangent singularity handling, and numeric-display tolerances before the instrument can be verified as fully specified.

- The stated formula correctly defines the unit-circle point as (cos(theta), sin(theta)), but it does not explicitly define tan(theta) = sin(theta)/cos(theta).

- The angle input/output unit is unspecified; the instrument must explicitly distinguish degrees from radians and state which unit is used internally.

- The reference-angle convention is unspecified; it should define the reference angle as the acute angle to the x-axis, normally in [0, pi/2].

- The meaning of 'angle in/out' is ambiguous: it should specify whether angles are normalized to [0, 360 degrees), (-180 degrees, 180 degrees], [0, 2*pi), or another interval.

## Units and conventions

- Test vectors explicitly identify whether the input is in degrees or radians.

- Trigonometric functions are evaluated using radians internally, with degrees converted by theta_radians = theta_degrees * pi/180.

- The reference angle is the nonnegative acute angle between the terminal ray and the x-axis, including boundary values 0 and pi/2.

- Coordinates are dimensionless; tangent is dimensionless.

- At angles where cos(theta) = 0, tan(theta) is undefined rather than an arbitrarily large finite number.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "angle": 0,
    "angle_unit": "degrees"
  },
  "expected_outputs": {
    "radians": 0,
    "degrees": 0,
    "coordinate": {
      "x": 1,
      "y": 0
    },
    "sin": 0,
    "cos": 1,
    "tan": 0,
    "reference_angle_degrees": 0
  },
  "working": "1. Convert degrees to radians: 0 * pi/180 = 0.\n2. Unit-circle point: (cos(0), sin(0)) = (1, 0).\n3. Tangent: tan(0) = sin(0)/cos(0) = 0/1 = 0.\n4. Reference angle: 0 degrees."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The singular tangent case requires explicit undefined-result handling, and the specification does not define angle sign or rotation-direction conventions. A finite tangent at π/2 or a reversed point for −90° would be an implementation failure.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/unit-circle-explorer/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/unit-circle-explorer/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/unit-circle-explorer/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche6/tranche6-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`