cot

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. It states the input ('angle in radians') and the mathematical operation, but does not cover potential edge cases (e.g., behavior at angles where tan is zero, leading to undefined results), error handling, or output format. This leaves significant gaps for a tool performing a mathematical function with potential domain restrictions.

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 extremely concise and front-loaded: it directly states the tool's function in the first phrase, followed by domain and category in parentheses. Every sentence (effectively one main clause) earns its place by providing essential information without redundancy or fluff, making it highly efficient.

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 tool's low complexity (single parameter, no annotations, no output schema), the description is minimally adequate. It covers the basic operation and input semantics but lacks details on behavior, error cases, and output. For a mathematical function with potential domain issues, more context would be beneficial, making it just sufficient but with clear gaps.

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, so the description must compensate. It adds meaning by specifying that the parameter is an 'angle in radians', which clarifies the unit and type beyond the schema's generic 'number'. However, it does not provide further details like valid ranges or constraints, resulting in a baseline score of 3 as it partially compensates for the low schema coverage.

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 cotangent (1/tan) of an angle in radians.' It specifies the verb ('calculate'), resource ('cotangent'), and clarifies the mathematical relationship (1/tan). However, it does not explicitly differentiate from sibling tools like 'coth' (hyperbolic cotangent) or 'acot' (inverse cotangent), which are present in the sibling list, preventing a score of 5.

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 minimal guidance: it mentions the domain ('trigonometry') and category ('basic_functions'), which implies context but does not specify when to use this tool versus alternatives like 'tan' or 'coth'. No explicit when-to-use, when-not-to-use, or alternative tool references are included, leaving usage unclear beyond basic categorization.

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