Select the parametric equations matching with the following graph.
A)Involute of circle: $$x = \frac { 1 } { 5 } ( \cos \theta + \Theta \sin \theta ) , y = \frac { 1 } { 5 } ( \sin \theta - \Theta \cos \theta )$$
B)Involute of circle: $x = \frac { 1 } { 5 } ( \cos \theta + \Theta \sin \theta ) , y = \frac { 1 } { 5 } ( \sin \theta + \Theta \cos \theta )$
C)Involute of circle: $x = \frac { 1 } { 5 } ( \cos \Theta - \Theta \sin \theta ) , y = \frac { 1 } { 5 } ( \sin \theta - \Theta \cos \theta )$
D)Involute of circle: $x = \frac { 1 } { 5 } ( \cos \theta - \Theta \sin \theta ) , y = \frac { 1 } { 5 } ( \sin \theta + \Theta \cos \theta )$
E)Involute of circle: $x = \frac { 1 } { 5 } ( \cos \theta + \Theta \sin \theta ) , y = \frac { 1 } { 5 } ( \cos \theta - \Theta \sin \theta )$

Question

Select the parametric equations matching with the following graph.​  ​
A)Involute of circle: $$x = \frac { 1 } { 5 } ( \cos \theta + \Theta \sin \theta ) , y = \frac { 1 } { 5 } ( \sin \theta - \Theta \cos \theta )$$ 
B)Involute of circle: $x = \frac { 1 } { 5 } ( \cos \theta + \Theta \sin \theta ) , y = \frac { 1 } { 5 } ( \sin \theta + \Theta \cos \theta )$ 
C)Involute of circle: $x = \frac { 1 } { 5 } ( \cos \Theta - \Theta \sin \theta ) , y = \frac { 1 } { 5 } ( \sin \theta - \Theta \cos \theta )$ 
D)Involute of circle: $x = \frac { 1 } { 5 } ( \cos \theta - \Theta \sin \theta ) , y = \frac { 1 } { 5 } ( \sin \theta + \Theta \cos \theta )$ 
E)Involute of circle: $x = \frac { 1 } { 5 } ( \cos \theta + \Theta \sin \theta ) , y = \frac { 1 } { 5 } ( \cos \theta - \Theta \sin \theta )$

Quizplus · Accepted Answer

The graph is a classic example of an involute of a circle, which can be parameterized by the following equations:
x = r(cos(t) + t sin(t))
y = r(sin(t) - t cos(t))
where r is the radius of the circle. The graph matches with the parameterization given by choice A.

Select the Parametric Equations Matching with the Following Graph x=15(cos⁡θ+Θsin⁡θ),y=15(sin⁡θ−Θcos⁡θ)x = \frac { 1 } { 5 } ( \cos \theta + \Theta \sin \theta ) , y = \frac { 1 } { 5 } ( \sin \theta - \Theta \cos \theta )x=51​(cosθ+Θsinθ),y=51​(sinθ−Θcosθ)

Select the Parametric Equations Matching with the Following Graph $x = \frac { 1 } { 5 } ( \cos \theta + \Theta \sin \theta ) , y = \frac { 1 } { 5 } ( \sin \theta - \Theta \cos \theta )$