How do you find the distance travelled from t=0 to #t=2pi# by an object whose motion is #x=cost, y=sint#?

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How do you find the distance travelled from t=0 to #t=2pi# by an object whose motion is #x=cost, y=sint#?

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Answer 1 · 2017-03-09T11:31:03

#2 pi# units

Explanation:

That is circular motion about a unit circle, a complete cycle happens in period #t = 2 pi#. So the distance is the circumference of the unit circle # = 2 pi cdot 1#.

As it's labelled a calculus question, if you want to do an an arc length calculation, then:

#int_0^(2 pi) sqrt((dot x)^2 + (dot y)^2) dt #

#= int_0^(2 pi) sqrt((- sin t)^2 + (cos t)^2) dt #

#= int_0^(2 pi) dt = 2 pi #

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How do you find the distance travelled from t=0 to #t=2pi# by an object whose motion is #x=cost, y=sint#?

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