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islobodan

Crucher MCP

atan

Read-onlyIdempotent

Calculates the arctangent of a number, returning the angle in degrees by default or radians when specified.

Instructions

Arctangent. Result in degrees by default, or radians with unit param.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
valueYes
unitNo

Implementation Reference

  • The 'atan' tool handler function. It computes the arctangent of a value using Math.atan(), then converts the result from radians to degrees (or keeps radians) based on the unit parameter or global angle mode.
    /**
     * Calculates the inverse tangent (arctangent) of a value.
     * @param {Object} args - The arguments object.
     * @param {number} args.value - The value.
     * @param {string} [args.unit] - The unit ("degrees" or "radians").
     * @returns {number} The angle whose tangent is value.
     */
    atan: ({ value, unit }) => fromRadians(Math.atan(value), unit),
  • The 'atan' tool schema registration in the toolsAll array. Defines name 'atan', description, and inputSchema requiring a 'value' (number) with optional 'unit' enum ('degrees', 'radians').
    {
        name: "atan",
        annotations: {
            title: "Arctangent",
            readOnlyHint: true,
            destructiveHint: false,
            idempotentHint: true,
            openWorldHint: false,
        },
        description:
            'Arctangent. Result in degrees by default, or radians with unit param.',
        inputSchema: {
            type: "object",
            properties: {
                value: { type: "number" },
                unit: { type: "string", enum: ["degrees", "radians"] },
            },
            required: ["value"],
        },
    },
  • cruncher.js:74-74 (registration)
    The 'atan' tool is registered in the 'standard' tool tier, making it available when CRUNCHER_TOOL_SET is 'standard' or 'full'.
    "sine", "cosine", "tangent", "asin", "acos", "atan",
  • cruncher.js:121-121 (registration)
    'atan' listed in TRIG_TOOLS array, marking it as a trig function that runs in the main thread and is cacheable.
    const TRIG_TOOLS = ["sine", "cosine", "tangent", "asin", "acos", "atan"];
  • cruncher.js:134-134 (registration)
    'atan' listed in MAIN_THREAD_TOOLS set, ensuring it executes directly on the main thread without worker overhead.
    "sine", "cosine", "tangent", "asin", "acos", "atan",
Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

The description adds the unit behavior (default degrees, option for radians) beyond the annotations which only indicate read-only, idempotent, non-destructive. No contradiction with annotations.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

Two sentences, no waste. Front-loaded with the core purpose 'Arctangent' followed by critical behavior. Every sentence serves a purpose.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness3/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given the low complexity and good annotations, the description covers the key unit behavior. However, it omits the result range (e.g., -90 to 90 degrees), input domain, and edge cases, which would be helpful for a math function with no output schema.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters2/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description must compensate. It mentions 'unit param' but adds little beyond the enum values 'degrees' and 'radians' already in schema. The 'value' parameter is not explained beyond the schema type.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly identifies the function as arctangent and specifies the output unit behavior (degrees default, radians optional). This distinguishes it from sibling trig functions like sine, cosine, and tangent.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

No explicit guidance on when to use this tool versus alternatives. The description only implies usage context through the unit parameter, but lacks when-not-to-use or alternative suggestions.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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