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IBM

MCP Math Server

by IBM

acsc

Calculate the arccosecant (inverse cosecant) of a number to find the angle whose cosecant equals that value. Use this trigonometric function for angle determination in mathematical computations.

Instructions

Calculate arccosecant (inverse cosecant). (Domain: trigonometry, Category: inverse_functions)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
valueYes
Behavior2/5

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

No annotations are provided, so the description carries the full burden of behavioral disclosure. The description only states what the tool calculates, with no information about error handling (e.g., for invalid inputs like |value| < 1), output format (degrees/radians), precision, or computational characteristics. For a mathematical function with potential domain restrictions, this is a significant gap in behavioral transparency.

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?

The description is extremely concise—just one sentence with parenthetical context—and front-loads the core purpose. Every word earns its place: 'Calculate arccosecant (inverse cosecant)' establishes the operation, and '(Domain: trigonometry, Category: inverse_functions)' provides helpful categorization without redundancy. No wasted words or unnecessary elaboration.

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

Completeness2/5

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

Given the tool's mathematical nature and lack of annotations/output schema, the description is incomplete. It doesn't address key contextual elements: parameter semantics, return value (angle in radians/degrees?), domain restrictions, or error conditions. While concise, it leaves too many open questions for effective tool use, especially compared to more thoroughly documented sibling tools in the list.

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?

The input schema has 0% description coverage, and the description provides no information about the 'value' parameter. It doesn't explain what 'value' represents (e.g., a real number, the cosecant of an angle), valid ranges (|value| ≥ 1 for real arccosecant), units, or special cases. With one undocumented parameter and no compensation in the description, this falls below the baseline expectation.

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

Purpose4/5

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

The description clearly states the tool's purpose: 'Calculate arccosecant (inverse cosecant)', which is a specific mathematical operation. It also provides domain context ('Domain: trigonometry, Category: inverse_functions'), which helps distinguish it from other mathematical tools. However, it doesn't explicitly differentiate from sibling tools like 'asec' or 'acot', which are also inverse trigonometric functions.

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?

The description provides no guidance on when to use this tool versus alternatives. While the domain/category tags imply it's for trigonometric calculations, there's no mention of when arccosecant is appropriate compared to other inverse trigonometric functions (like arcsin or arccos) or how it relates to sibling tools like 'csc' (cosecant). No prerequisites, input constraints, or typical use cases are described.

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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