LEARN · EXPLAIN · REVISE

Let x be measured in radians. Find the least positive x at which y reaches its maximum. Write x = cπ and enter the number c.

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

TOPIC 01

Trigonometric ratios and function graphs

The horizontal shift is π/6, and one quarter of the period is π/4. Their sum is 5π/12. For a decimal answer, use at least six decimal places.

PREDICT → MOVE → EXPLAIN

See amplitude, period and phase together.

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

Try it. Leave your reasoning visible.

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

01 / Transfer#Your turn

Let x be measured in radians. Find the least positive x at which y reaches its maximum. Write x = cπ and enter the number c.

y=2\sin\left(2x-\frac\pi3\right)

Working and explanation

BUILD THE REASONING

Hint 1

A maximum requires the angle inside sine to equal π/2 + 2πn.

Hint 2

Add π/3 before dividing by 2. Then select the least positive solution.

Worked solution

Set the argument to the peak angles of sine.
$2x-\frac\pi3=\frac\pi2+2\pi n$
Solve the linear equation for x.
$x=\frac{5\pi}{12}+\pi n,\quad n\in\mathbb Z$
The preceding solution is negative; divide the first positive solution by π.
$c=\frac5{12}\approx0.416666667$

c = 5/12 ≈ 0.416666667, so the first positive peak is at x = 5π/12.

Checks and common pitfalls: The horizontal shift is π/6, and one quarter of the period is π/4. Their sum is 5π/12. For a decimal answer, use at least six decimal places.

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