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)= &lt; 2 cos⁡ t, 2 sin⁡ t, t &gt;.

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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)= &amp;lt; 2 cos⁡ t, 2 sin⁡ t, t &amp;gt;.

faldduE · Accepted Answer

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)= &amp;lt; 2 cos⁡ t, 2 sin⁡ t, t &amp;gt;. 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―

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 >.

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