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IBM

MCP Math Server

by IBM

acos_degrees

Calculate arccosine values in degrees for trigonometric problems. Use this tool to find angle measures from cosine ratios in geometry and physics applications.

Instructions

Calculate arccosine with result in degrees. (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. It states the calculation behavior but lacks critical details: input domain constraints (e.g., value must be between -1 and 1), error handling, output range (typically 0 to 180 degrees), or precision. For a mathematical tool with no annotation coverage, this is insufficient.

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

Conciseness4/5

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

The description is concise and front-loaded with the core purpose. The additional domain/category context is brief and relevant. No wasted words, though it could be more informative without sacrificing brevity.

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 no annotations, 0% schema coverage, and no output schema, the description is incomplete. It omits essential details: parameter semantics, input constraints, output format, and error conditions. For a mathematical function, this leaves significant gaps for an AI agent to use it correctly.

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%, and the description adds no parameter information beyond the schema. It does not explain what 'value' represents (e.g., cosine value), its valid range, or units. With one undocumented parameter, the description fails to compensate for the schema's lack of descriptions.

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 arccosine with result in degrees.' It specifies the mathematical function (arccosine), the output unit (degrees), and provides domain/category context. However, it does not explicitly differentiate from its sibling 'acos' (which likely returns radians), missing full sibling distinction.

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. It mentions the domain (trigonometry) and category (inverse_functions), but offers no explicit when/when-not instructions or references to sibling tools like 'acos' or 'asin_degrees' for comparison.

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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