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IBM

MCP Math Server

by IBM

sin_series

Compute sine values using Taylor series expansion with specified precision. Enter angle x and term count n to calculate sin(x) through numerical series approximation.

Instructions

Compute sine function using Taylor series expansion (Domain: numerical, Category: series)

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
xYes
nYes
Behavior2/5

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

With no annotations provided, the description carries the full burden of behavioral disclosure. It states the computation method (Taylor series expansion) which implies approximation behavior rather than exact calculation, but doesn't specify accuracy characteristics, convergence conditions, error bounds, or computational complexity. For a numerical approximation tool with zero annotation coverage, this represents significant gaps in behavioral transparency.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness4/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is appropriately concise with a single sentence containing the core computation method and domain/category metadata. It's front-loaded with the main purpose ('Compute sine function using Taylor series expansion') and wastes no words. The parenthetical domain/category information could be integrated more smoothly but doesn't detract significantly from readability.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness2/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

Given a 2-parameter numerical computation tool with no annotations and no output schema, the description is incomplete. It doesn't explain what the tool returns (approximated sine value), error characteristics, or practical usage considerations. For a Taylor series implementation, important context like convergence radius, typical 'n' values for reasonable accuracy, and comparison to direct sine computation is missing, making this inadequate for informed tool selection.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters2/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

The schema has 0% description coverage, so the description must compensate but fails to do so adequately. It doesn't explain what parameters 'x' and 'n' represent (presumably angle and series terms count), their units (radians vs degrees), valid ranges, or the relationship between 'n' and accuracy. The description adds no parameter semantics beyond what's implied by 'Taylor series expansion' for those familiar with the method.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool's purpose: 'Compute sine function using Taylor series expansion' with domain and category context. It specifies the mathematical method (Taylor series) and function (sine), distinguishing it from simpler trigonometric tools like 'sin' or 'sin_degrees' in the sibling list. However, it doesn't explicitly differentiate from 'cos_series' or other series-based siblings beyond naming the sine function.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

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

The description provides minimal usage guidance. It mentions 'Domain: numerical, Category: series' which gives some context about input types and mathematical category, but offers no explicit guidance on when to use this tool versus alternatives like 'sin', 'sin_degrees', or other approximation methods. There's no mention of trade-offs between accuracy and computational cost, or when Taylor series approximation is preferable to direct computation.

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

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