arccos

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

No annotations are provided, so the description carries the burden; it usefully discloses that the return is in radians, which is the key behavioral fact for a trig function. It omits the domain restriction [-1, 1] and what happens for out-of-range input, leaving a real but modest gap for a pure math function with no side effects.

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?

Two short sentences, zero waste: the core behavior plus its unit is front-loaded, and the batch_calc pointer follows. Nothing is repeated from the schema.

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 single-parameter, side-effect-free math function with no output schema, stating the result unit and the batch alternative is nearly sufficient. The one missing element is the accepted input range, which an agent could otherwise stumble on.

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 there is a single parameter already documented as 'The number to find the arccosine of'; the description adds no syntax, range, or format detail beyond that. Baseline 3 applies since the schema does the heavy lifting and the description does not compensate for the missing domain constraint.

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?

States a specific verb (calculates) and resource (arccosine of a number), and disambiguates the result unit with '(in radians)' — meaningful given siblings like degreesToRadians and radiansToDegrees. The function name plus unit makes it distinguishable from arcsin/cos/tan without opening the schema.

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?

Explicitly routes multi-step or multi-operation work to batch_calc, which is a clear alternative-selection rule. It does not state exclusions or prerequisites (e.g., input must be in [-1, 1]), so it stops short of full when/when-not guidance.

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