LEARN · EXPLAIN · REVISE

Find tangent after a half turn.

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 / Transfer#Your turn

\tan\alpha=4;\quad\tan(\pi+\alpha)

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Use unit-circle symmetry and periodicity; determine the sign before simplifying.

Hint 2

Both sine and cosine change sign.

Worked solution

Use unit-circle symmetry and periodicity; determine the sign before simplifying.
Calculate or simplify this relation.
$\tan(\pi+\alpha)=\tan\alpha=4$
Their quotient stays unchanged when defined.

The requested value is 4.

Checks and common pitfalls: Their quotient stays unchanged when defined.

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.