2024 IGCSE Additional Mathematics October/November 0606/12 Q1

The curve \(y=a\cos bx+c\), where \(a\), \(b\) and \(c\) are integers, passes through the points \(\left(-\dfrac\pi6,-2\right)\) and \(\left(\dfrac\pi9,\dfrac12\right)\). The curve has a period of \(\dfrac{2\pi}3\).

1. Find the values of \(a\), \(b\) and \(c\).[4]
2. Find the least value of \(y\) on the curve for \(0\leq x\leq\dfrac\pi2\), and state the value of \(x\) at which this occurs.[3]