An object with weight $W$ is dragged along a horizontal plane by a force acting along a rope attached to the object. If the rope makes an angle $t$ with the plane, then the magnitude of the force is $\displaystyle F=\frac{\mu W}{\mu \sin{t}+\cos{t}}$, where $\mu$ is a constant called the coefficient of friction. Let $W=25$ lb and $\mu=0.5$.

(a) Find the rate of change of F with respect to $t$.
$F'(t) =$

(b) When is this rate of change equal to zero? Round your answer to the nearest hundredth.
$t=$ rad.