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

With no annotations, the description carries the behavioral burden. It discloses the return shape (equation and features) but does not state determinism, side effects, error behavior, or the effect of the locale parameter on rendered output.

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 a single well-structured paragraph that front-loads purpose, then inputs, returns, and use case. The input list partly repeats schema descriptions, but it remains efficient and readable.

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?

For a 7-parameter computational tool with no output schema, the description adequately explains the return values and teaching context. It misses the locale parameter and does not provide sibling routing, but those gaps are minor relative to the schema coverage.

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?

Schema description coverage is 100%, so the baseline is 3. The description adds value by mapping parameters into the formula y = A·f(ωx+φ)+k and explaining what features are derived, though it omits the locale parameter present in the schema.

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 states a specific resource (trigonometric functions and the unit circle) and explains what the tool returns (equation and features). It is clear enough for an agent to distinguish from generic graph tools, but it does not explicitly differentiate itself from siblings like function-grapher or geometry-lab.

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?

It gives explicit intended use: 'Use this for teaching trigonometry, periodic functions and graph transformations.' This is clear context for when to select it, though it names no alternatives or exclusions.

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