LEARN · EXPLAIN · REVISE

Write the least positive period as cπ. Find c.

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

TOPIC 01

Trigonometric ratios and function graphs

Frequency 3 divides the period; it does not multiply it.

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=\cos(3x),\quad x\text{ in radians}

Working and explanation

BUILD THE REASONING

Hint 1

Cosine repeats after an argument change of 2π.

Hint 2

Solve 3T=2π.

Worked solution

c=2/3.

Checks and common pitfalls: Frequency 3 divides the period; it does not multiply it.

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