2025 TKSS PRELIMS P1 Q10

It is given that \(y = a\cos bx + c\), for \(0 \leq x \leq \frac{4}{3}\pi\), where \(a\), \(b\) and \(c\) are positive integers.

The period of \(y\) is \(\frac{2}{3}\pi\) and the maximum and minimum value of \(y\) is 5 and 1 respectively.

1. State the values of \(a\), \(b\) and \(c\).[3]
2. Sketch the graph of \(y = a\cos bx + c\) for \(0 \leq x \leq \frac{4}{3}\pi\).[3]
3. Hence, find the value of constant \(d\) such that the equation \(\cos bx = d\) will have 2 solutions.[2]