Answer
See answers.
Work Step by Step
Suppose the pendulum starts at maximum displacement. The equation of motion is known.
$$\theta=\theta_o cos \omega t=\theta_o cos 2 \pi f t $$
The initial angle $\theta_o $ is given as 12 degrees, but we may convert that to radians, and find an expression for the angular displacement in radians at any time t.
$$\theta=(12^{\circ})\frac{\pi \;rad}{180^{\circ}} cos 2 \pi (2.5\;Hz) t $$
$$\theta=\frac{\pi}{15} cos 5 \pi t $$
Now, evaluate this at the 3 times that are stated.
a.
$$\theta(0.25\;s)= \frac{\pi}{15} cos 5 \pi (0.25\;s)=-0.15\;rad$$
b.
$$\theta(1.60\;s)= \frac{\pi}{15} cos 5 \pi (1.60\;s)=\frac{\pi}{15}\;rad$$
This makes sense, because the time is exactly 4 periods, so the pendulum has returned to its starting point.
c.
$$\theta(500\;s)= \frac{\pi}{15} cos 5 \pi (500\;s)=\frac{\pi}{15}\;rad$$
This makes sense, because the time is exactly 1250 periods, so the pendulum has returned to its starting point.