Question: The cycloid generated by the unit circle has parametrization r(t) = (t sint, 1 - cost) (a) Find the value of t in [0,27] where

The cycloid generated by the unit circle has parametrization

r(t) = (t sint, 1 - cost) (a) Find the value of t in [0,27] where the speed is at a maximum. (b) Show that

r(t) = (t sint, 1 - cost) (a) Find the value of t in [0,27] where the speed is at a maximum. (b) Show that one arch of the cycloid has length 8. Recall the identity sin(1/2) = (1 - cost)/2.

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