Torque and Work Practice Test

A gyroscope with its axis tilted precesses with a constant angular speed about a vertical axis. The gravitational force exerts a torque on the gyroscope, causing the precession. What is the work done by this gravitational torque during one complete precession cycle?

A net torque given by $$\tau = \tau_0 \sin(\theta)$$ is applied to a rotor, where $$\tau_0$$ is a positive constant. What is the work done by this torque as the rotor moves from an angular position of $$\theta = 0$$ to $$\theta = \pi$$ radians?