LEARN · EXPLAIN · REVISE

Write the least positive period as cπ; find c.

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

高一必修第一册(A版).pdf · 5.6 · PDF 238 / printed page 231

TOPIC 01

The function y=A sin(ωx+φ)

Build understanding of the function y=a sin(ωx+φ) through definitions, contrasting cases and justified applications.

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

01 / Standard#Worked example

y=3\sin(2x+\pi/4)

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Separate amplitude, internal frequency, phase and vertical shift.

Hint 2

Phase does not change the cycle length.

Worked solution

The requested value is 1.

Checks and common pitfalls: The nonzero amplitude and frequency guarantee a nonconstant sinusoid.

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

Teacher preparation and assessment

Use the function y=a sin(ωx+φ) with explicit angle units and domains.
Scale and cycle: Amplitude is |A|; for a nonconstant graph the least positive period is 2π/|ω|.
Phase shift: Factor ω to read the horizontal shift −φ/ω.
Close with: conditions → representation → reasoning → check.

Expected reasoning: Amplitude is |A|; for a nonconstant graph the least positive period is 2π/|ω|.
Expected reasoning: Factor ω to read the horizontal shift −φ/ω.
Expected correction: A constant graph has no least positive period.