MediumCurves in space

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §12.2 Plane Motion: Projectiles and Cycloids, #20 · Multivariable Calculus · Curves in space

The slope of the cycloid is infinite at …: … \frac{dy}{dx} =…

This problem is about cycloids and related curves

The slope of the cycloid is infinite at $θ = 0$ :
$\frac{d y}{d x} = \frac{d y / d θ}{d x / d θ} = \frac{sin θ}{1 - cos θ} .$
By whose rule? Estimate the slope at $θ = \frac{1}{10}$ and $θ = - \frac{1}{10}$ . Where does the slope equal one?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §12.2 Plane Motion: Projectiles and Cycloids, #20

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