Answer
(a) 0.2 radians
(b) 1.45 rad/s
Work Step by Step
Step-1: It is given at $\theta = 0.2\cos (8t)$. $\cos$ function varies in the interval $[-1, 1]$. Thus, the maximum value of angular displacement will be when the $\cos$ function will amount to $1$. Thus, $\theta_{max} = 0.2\times 1 = 0.2$ radians. This will happen when $8t$ equals $0, \frac{3\pi}{16}, \frac{\pi}{4}, \dots$
Step-2: The rate of change of angular displacement with respect to time,
$$\frac{d\theta}{dt} = 0.2\frac{d}{dt}\cos(8t)=0.2\cdot(-\sin(8t))\cdot(8)$$
$$rate=\frac{d\theta}{dt}=-1.6\sin(8t)$$
Step-3: At $t=3s$, $rate = -1.6sin(8*3)=1.45$ radians/s.
