sum_difference_formulas

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 mentions the calculation method but does not disclose behavioral traits such as input constraints (e.g., numeric ranges for angles), output format, error handling, or computational limits. For a tool with no annotations, this leaves significant gaps in understanding its operation.

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 with the main purpose in the first sentence, followed by domain/category tags. There is no wasted text, and it efficiently communicates the core function without unnecessary details, though it could be slightly more informative.

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 trigonometric calculation tool with 3 parameters, 0% schema coverage, no annotations, and no output schema, the description is incomplete. It does not cover parameter meanings, behavioral aspects, or output details, making it inadequate for an agent to use the tool effectively without additional context.

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 0% description coverage, and the description does not explain the parameters (a, b, operation). It mentions 'sum and difference formulas' but does not clarify what a and b represent (e.g., angles in radians or degrees) or how the operation parameter affects the calculation. With low schema coverage, the description fails to compensate, leaving parameters largely undocumented.

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 trigonometric functions using sum and difference formulas.' It specifies the verb ('calculate'), resource ('trigonometric functions'), and method ('sum and difference formulas'). However, it does not differentiate from sibling tools like 'double_angle_formulas' or 'half_angle_formulas', which are also trigonometric identity tools, so it misses 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.

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

The description provides minimal guidance with the domain and category tags ('Domain: trigonometry, Category: identities'), but this is too vague to indicate when to use this tool versus alternatives. It lacks explicit when-to-use instructions, prerequisites, or comparisons to sibling tools like 'verify_sum_difference_formulas', which might be for verification rather than calculation.

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