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Match the Graph to a Set of Parametric Equations x=2cotθx = 2 \cot \theta

Question 35

Multiple Choice

Match the graph to a set of parametric equations.
 Match the graph to a set of parametric equations.    A)  Witch of Agnesi:  x = 2 \cot \theta   y = 2 \sin ^ { 2 } \theta   B)  Lissajous curve:  x = 3 \cos \theta   y = \sin 2 \theta   C)  Involute of circle  \begin{array} { l }  x = \cos \theta + \theta \sin \theta \\ y = \sin \theta - \theta \cos \theta \end{array}  D)  Evolute of ellipse:  x = 3 \cos ^ { 3 } \theta   y=5 \sin ^{3} \theta   E)   \begin{array}{l} x=\cot \theta \\ y=6 \sin \theta \cos \theta \end{array}


A) Witch of Agnesi:
x=2cotθx = 2 \cot \theta
y=2sin2θy = 2 \sin ^ { 2 } \theta

B) Lissajous curve:
x=3cosθx = 3 \cos \theta
y=sin2θy = \sin 2 \theta

C) Involute of circle
x=cosθ+θsinθy=sinθθcosθ\begin{array} { l } x = \cos \theta + \theta \sin \theta \\y = \sin \theta - \theta \cos \theta\end{array}
D) Evolute of ellipse:
x=3cos3θx = 3 \cos ^ { 3 } \theta
y=5sin3θy=5 \sin ^{3} \theta

E) x=cotθy=6sinθcosθ\begin{array}{l}x=\cot \theta \\y=6 \sin \theta \cos \theta\end{array}

Correct Answer:

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