A point on the rim of a rolling wheel of radius 2 traces the cycloid x = 2(t - sin t), y = 2(1…

Step 1. The rates. $\dfrac{dx}{dt} = 2(1 - \cos t)$ and $\dfrac{dy}{dt} = 2\sin t$.

Step 2. The slope. $\dfrac{dy}{dx} = \dfrac{\sin t}{1 - \cos t} = \cot\dfrac{t}{2}$.

Step 3. At $t = \dfrac{\pi}{3}$. $\cot\dfrac{\pi}{6} = \sqrt{3} = 1.7321$.

Step 4. At $t = \dfrac{\pi}{2}$. $\cot\dfrac{\pi}{4} = 1$.