Question

12.3.8 Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. r(t) = (5t sint+5 cos t)i + (5t cost-5 sint)j V2 sts2 The curve's unit tangent vector is (i+j+ K.

Answer 1

Y(u) = (st sint +50+) { +(54cost-5 Sint)j de star (t) = $ 5+ sink +5 cast, 5tcost-5Sint, 03 ef's sit + Steosta- 554t, 5cost-5t sint -5 cost ,03 Filt) = & Stcost, – 5t sint, o} HECH I J (Steast)?+ (-5tsuits? +02 Jast cose + 2st sin24 25+2(cos 2 + + Sinit) ✓ 2572 =56 Now, curves unit tangent vector is (t) = ŷ (t) = Ņ't) ştcost, – stsint, og 8(t) = cost, -sivt, og TCH) = $(4) = (cost li+[-Sint 1j+[ 0 ] 5t let r(t) = (g(t), h(t), o) where get) = 5tsink+s cost Alt) - Stcost-ssink then, -- S. 814) P4 (21492 de ſ15tcost) + (-stsinte at Va 32 $25t2 at V2 5tdie 5+2 2 = 5(2-1) = 5