acot

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 tool calculates arccotangent but does not disclose behavioral traits such as input validation (e.g., handling of invalid values like zero), output range (e.g., radians or degrees), error handling, or performance characteristics. This is a significant gap for a mathematical function tool.

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

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

The description is concise and front-loaded, consisting of a single sentence that directly states the tool's purpose. There is no unnecessary information, making it efficient. However, it could be slightly improved by structuring it to include key details like parameter guidance.

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

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

Given the complexity of a mathematical function with no annotations, no output schema, and low parameter coverage, the description is incomplete. It lacks essential context such as output format, error conditions, and mathematical properties (e.g., branch cuts or range of results). This makes it inadequate for reliable tool invocation.

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

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

The input schema has 1 parameter with 0% description coverage. The description does not add any meaning beyond the schema—it does not explain what 'value' represents (e.g., a real number, expected units, or domain restrictions like avoiding zero for cotangent). With low schema coverage, the description fails to compensate, leaving the parameter semantics unclear.

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

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 arccotangent (inverse cotangent).' It specifies the mathematical function and its domain (trigonometry) and category (inverse_functions). However, it does not explicitly differentiate from sibling tools like 'acoth' (inverse hyperbolic cotangent) or 'atan' (inverse tangent), which could be relevant alternatives.

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

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 and category but does not specify use cases, prerequisites, or comparisons to sibling tools like 'acoth' or 'atan'. This leaves the agent without explicit usage instructions.

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