The official graph has minimum 0, maximum 4, and a maximum at x=5π/3. Find a,b.

01 / Standard#Your turn

y=a\sin(x-\pi/6)+b

Official paper · jm01-2023 · I.14 · PDF 3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Use the midpoint and half-range of the vertical values.

Hint 2

At 5π/3 the sine is −1.

Worked solution

Recover the midline and amplitude.
$b=(4+0)/2=2,\quad|a|=(4-0)/2=2$
Use the maximum point to determine the sign.
$4=a\sin(3\pi/2)+2=-a+2\implies a=-2$

B: a=−2, b=2.

Checks and common pitfalls: Amplitude gives |a|, not its sign.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Recover the midline and amplitude.
$b=(4+0)/2=2,\quad|a|=(4-0)/2=2$
Use the maximum point to determine the sign.
$4=a\sin(3\pi/2)+2=-a+2\implies a=-2$

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

2023 JM01