Consider the helix represented investigation by the vector-valued function r(t)= < 2 cos t, 2 sin t, t >. Solve for t in the relationship derived in p

sanuluy 2020-10-28 Answered
Consider the helix represented investigation by the vector-valued function r(t)= < 2 cos t, 2 sin t, t >. Solve for t in the relationship derived in part (a), and substitute the result into the original set of parametric equations. This yields a parametrization of the curve in terms of the arc length parameter s.
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Brittany Patton
Answered 2020-10-29 Author has 100 answers
The curve in terms of arc legth is r(s)=2 cos (s5)i + 2 sin (s5)j + s5k. Given: The function r(t)= < 2 cos t, 2 sin t, t > s=(5t) Calculate: The given vector-function for the path is r(t)= < 2 cos t, 2 sin t, t >........(1) The length of the curve is s=(5t)
t= s5t Substituting this value of t in equation (1), we get r(s)= 2 cos (s5t), 2 sin (s5t), s5t Or r(s)=2 cos (s5)i + 2 sin (s5)j + s5k. Thus, the curve in terms of arc length is r(s)=2 cos (s5)i + 2 sin (s5)j + s5k.
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