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

Annotations already declare readOnlyHint, idempotentHint, and destructiveHint false. The description adds useful behavioral context by defining the principal value range (-90°, 90°) / (-π/2, π/2) and the inverse relationship tan(θ) = x, which explains what the result represents. It doesn't detail output formatting but is sufficient for a read-only calculator.

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 two tight sentences with no filler. It front-loads the core purpose, follows with the mathematical definition and range, and ends with a clear pointer to an alternative. Every sentence earns its place.

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 simple calculator tool with strong annotations and no output schema, the description sufficiently explains what the result is (an angle), the possible unit options, the principal value constraint, and the key alternative. No critical context is missing for an agent to correctly select and invoke the tool.

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%, and the schema already fully describes both parameters, including domain and defaults. The description adds minimal new parameter meaning beyond what is in the schema (e.g., 'any real number' is already in the x description), so it does not elevate above the baseline.

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 verb ('Compute') and resource ('arctan(x)'), clearly identifies the mathematical function (inverse tangent), and notes the degrees/radians options. It also differentiates from two-argument arctan by explicitly naming atan2, which distinguishes it from related tools.

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 gives clear guidance on when to use this single-argument arctan tool versus atan2, including an explicit exclusion: 'For two-argument arctan that resolves the full circle, use atan2 instead.' This is a strong when-not/alternative statement.

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