Suppose a 15-centimeter pendulum moves according to the equation $\theta = 0.6 \cos 8 t$ where $\theta$ is the angular displacement from the vertical in radians and $t$ is the time in seconds. Determine the rate of change of $\theta$ when $t = 7$ seconds. Round your answer to four decimal places.
A) $2.5034$ radians per second
B) $3.6185$ radians per second
C) $0.3129$ radians per second
D) $3.1535$ radians per second
E) $4.1724$ radians per second

Question

Quizplus · Accepted Answer

The rate of change of $\theta$ is given by the derivative of $\theta$ with respect to $t$, which is $\frac{d\theta}{dt} = -0.6 \cdot 8 \sin 8 t$. When $t = 7$, $\frac{d\theta}{dt} = -0.6 \cdot 8 \sin 56 \approx -2.5034$ radians per second.

Suppose a 15-Centimeter Pendulum Moves According to the Equation θ=0.6cos⁡8t\theta = 0.6 \cos 8 tθ=0.6cos8t

Suppose a 15-Centimeter Pendulum Moves According to the Equation $\theta = 0.6 \cos 8 t$