LEARN · EXPLAIN · REVISE

With x measured in radians, what is the least positive period?

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

TOPIC 01

Trigonometric ratios and function graphs

In a width of 2π along the x-axis this curve completes two cycles. Its amplitude is 3, independently of its period.

PREDICT → MOVE → EXPLAIN

Predict the number of cycles and the horizontal shift. Switch angle units without changing the curve.

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

01 / Standard#Your turn

y=3\sin(2x)

Working and explanation

BUILD THE REASONING

Hint 1

The factor 3 affects vertical distances, not the period.

Hint 2

Find the smallest positive T for which the angle 2x advances by 2π.

Worked solution

C: the least positive period is π radians.

Checks and common pitfalls: In a width of 2π along the x-axis this curve completes two cycles. Its amplitude is 3, independently of its period.

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