Reconstruct a sine model
8 written marks
A wave has equation \(y=a+b\sin(cx)\), where \(b,c\gt 0\). Its maximum is 9, its minimum is 1 and its least positive period is \(\displaystyle \frac{4\pi }{3}\).
Part a · 3 marks
Find \(a,b,c\).
Part b · 2 marks
Find the first maximum point after \(x=0\) and the next minimum point.
Part c · 3 marks
Find all \(\displaystyle x\in [0, \frac{4\pi }{3}]\) for which \(y=7\).
Complete-answer checking, worked solutions and indicative written criteria.
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