Question

please solve and show steps so i can follow

4. Consider the space curve given by r(t) = (36,4 cost, 4 sint). If you start at the point (0,4,0) and travel in the positive direction (increasing t) for 10 units, where are you? Give both an exact answer and an answer rounded to two decimal places.

Answer 1

Given space caure, 8C+) = (3+, 4 lost; sint) * initially at the point <0,4, OY => 3t =0 3t =0 4 lost = 4 ; 4 Sint=0 t=0 سید now ce travel in the positive direction increasing t for 10 cenits. now, t = tot 10 (+ = + +10 and to ť=10 nowo, 3ť = 3(10) = 30 09818 3.9392 4 Cost = h Cos (10) = 4(6.9848) 4 sint = 4 sin (10) = 4(0.1736) = 0.6946. positive direction i now, by travelling in ents from point (0,4, 07 by increasing "t" by to units, we are at <3 (10), 4605(10), 4 sin (ro)) <30; 3.9392, 0.69467/ exact answer 7 Hanscoer 230, 3.94,0.69) rounded to two decimal places.