LEARN · EXPLAIN · REVISE

Evaluate cos 420° without a calculator.

Read the idea, work independently, then explain what changed.

高一必修第一册(A版).pdf · 5.3 · PDF 195 / printed page 188

TOPIC 01

Reduction formulas

Build understanding of reduction formulas through definitions, contrasting cases and justified applications.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Foundation#Your turn

\cos420^{\circ}

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Remove one full turn.

Hint 2

420° and 60° have the same terminal ray.

Worked solution

The requested value is 0.5.

Checks and common pitfalls: Cosine is unchanged by a full turn.

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment

Use reduction formulas with explicit angle units and domains.
Symmetry: Reflections determine which coordinate changes sign.
Periodicity: A full turn preserves sine and cosine; a half turn preserves tangent when defined.
Close with: conditions → representation → reasoning → check.

Expected reasoning: Reflections determine which coordinate changes sign.
Expected reasoning: A full turn preserves sine and cosine; a half turn preserves tangent when defined.
Expected correction: A reflected cosine often changes sign.