Select the curve represented by the parametric equations.
Curtate cycloid: $$x = 4 \Theta - 2 \sin \theta , y = 4 - 2 \cos \theta$$
A)
B)
C)
D)

Question

Select the curve represented by the parametric equations. ​
Curtate cycloid: $$x = 4 \Theta - 2 \sin \theta , y = 4 - 2 \cos \theta$$ ​
A)​ 
B)​ 
C)​ 
D)​

Quizplus · Accepted Answer

A curtate cycloid is a cycloid where the radius of the rolling circle is less than the radius of the fixed circle. The parametric equations of a curtate cycloid are:

x = r(θ - sinθ)
y = r(1 - cosθ)

where r is the radius of the rolling circle and θ is the parameter.

Looking at the given curves, only curve A fits these equations with r = 2. Therefore, A is the best choice for a curtate cycloid.

Select the Curve Represented by the Parametric Equations x=4Θ−2sin⁡θ,y=4−2cos⁡θx = 4 \Theta - 2 \sin \theta , y = 4 - 2 \cos \thetax=4Θ−2sinθ,y=4−2cosθ

Select the Curve Represented by the Parametric Equations $x = 4 \Theta - 2 \sin \theta , y = 4 - 2 \cos \theta$