For the cycloid described by the parametric equations x = 2(t - sint) and y = 2(1- cost), a) find the slope of the tangent line at t = b) find the value(s) for t where the tangent line to the curve is horizontal. c) set up (do not solve) a definite integral to find the area under two arches of the cycloid d) Describe what is happening to the curve at t= 27.

For the cycloid described by the parametric equations x = 2(t - sint) and y = 2(1- cost), a) find the slope of the tangent line at t = b) find the value(s) for t where the tangent line to the curve is horizontal. c) set up (do not solve) a definite integral to find the area under two arches of the cycloid d) Describe what is happening to the curve at t= 27.

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.6: Parametric Equations

Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...

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(2)
For the cycloid described by the parametric equations x = 2(t – sint) and y = 2(1- cost),
a) find the slope of the tangent line at t
3
b) find the value(s) for t where the tangent line to the curve is horizontal.
c) set up (do not solve) a definite integral to find the area under two arches of the cycloid
d) Describe what is happening to the curve at t= 2n .

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