Chapter 10, Problem 47RE

(a)

To determine

To Graph: The curve represented by the parametric equations $x=\cot \theta$ and $y=\sin 2\theta .$

(b)

To determine

To calculate: $dx/d\theta$, $dy/d\theta$, and $dy/dx$ at the given value of the parameter $\theta =\frac{\pi }{6}$ using a graphing utility tool.

(c)

To determine

To calculate: An equation of the tangent line to the curve at the given value of the parameter $\theta =\frac{\pi }{6}.$

(d)

To determine

To Graph: The curve and the tangent line from part (c).