Answer
a) $\frac{dy}{dt}=-2$
b) $\frac{dy}{dt}=-2\sqrt 2$
c) $\frac{dy}{dt}=-2\sqrt 3$
Work Step by Step
Using the chain rule, differentiate with respect to t. $$\frac{dy}{dt}=-sin(x)\times\frac{dx}{dt}$$
Plug in the known values of $\frac{dx}{dt}$ and x, then simplify. $$\frac{dy}{dt}=-4sin(\pi\div6)\\=-2$$
Plug in $\pi/4$ for b, to get $\frac{dy}{dt}=-4sin(\pi\div4)\\=-2\sqrt 2$
For part c, plug in $\pi/3$ for x to get $\frac{dy}{dt}=-4sin(\pi\div3)\\=-2\sqrt 3$
