- #1
ElijahRockers
Gold Member
- 270
- 10
Homework Statement
Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve.
Homework Equations
r(t) = (-3tcost)i + (3tsint)j + (2[itex]\sqrt{2}[/itex])t(3/2)k
0 ≤ t ≤ ∏
The Attempt at a Solution
So I found dr/dt (I think), which is
v(t) = (3tsint - 3cost)i + (3tcost + 3sint)j + (3[itex]\sqrt{2t}[/itex])k
This would be the tangent vector at 't', right?
So to find the unit tangent vector, I need to divide v(t) by its length, which would be the square root of its terms squared. This looks like it's going to be very ugly, but I tried to do it anyway. I got some huge radical that went all the way across the page.
The example showed that |v| was equal something much simpler, 3(t+1). My trig is not great, and I can't see how they got it down that small. Is there some trig identity I'm overlooking?
By the way, I am not taking any classes, this is independent study. I got this question from www.interactmath.com , Thomas' Calculus, 12e - Chapter 13, Section 3, Exercise 7
Thanks.