A peg stands on a turntable, 10 cm from its centre…

Step 1. To $A/2$. $\cos\omega t = 0.5$, so $\omega t = \pi/3$. That is a sixth of a turn: $t_1 = \dfrac{1.8\ \text{s}}{6} = 0.3\ \text{s}$.

Step 2. To the centre. $\cos\omega t = 0$, so $\omega t = \pi/2$. That is a quarter of a turn: $\dfrac{1.8\ \text{s}}{4} = 0.45\ \text{s}$.

Step 3. The second half. $0.45\ \text{s} - 0.3\ \text{s} = 0.15\ \text{s}$.