Find the coordinates of the point on the helix for arc lengths s = sqrt{5} and s = 4. Consider the helix represented investigation by the vector-valued function r(t)= < 2 cos t, 2 sin t, t >.

Harlen Pritchard 2020-11-23 Answered
Find the coordinates of the point on the helix for arc lengths s= 5 and s=4. Consider the helix represented investigation by the vector-valued function r(t)= < 2 cos t, 2 sin t, t >.
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faldduE
Answered 2020-11-24 Author has 109 answers
To calculate: The coordinates of the point on the helix for arc lengths s= 5 and s=4 For s= 5, the coordinates are 1.081 1.683 1 For s=4, the coordinates are 0.433 1.953 1.789 Given: The function r(t)= < 2 cos t, 2 sin t, t >. Calculation: The curve in terms of arc length is, r(s)=2 cos (s5)i + 2 sin (s5)j + s5k Case 1: s=5
r(5)=2 cos 55i + 2 sin (55)j + 55kt5k
=2 cos(1)i + 2 sin(1)j + 1k
=1.081i + 1.683j + 1k Case 2: s=4
r(4)=2 cos(45)i + 2 sin(45)j + 45k
= 0.433i + 1.953j + 1.789k Thus, for s= 5, the coordinates are(1.081, 1.683, 1) and for s=4, the coordinates are 0.433 1.953 1.789
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