curve r(t) = <t, cos(t), sin(t)>: find Frenet Frame at t =

[koalamath]

Problem:

Let the curve r(t) =< t,cos(t),sin(t) >.
a) What do we call the curve that is the graph of r = r(t)?
b) Find the Frenet Frame of the curve at t = ?/2.
c) Find the curvature of the curve at t = ?/2.
d) Find the parametric equations of the tangent line to the curve at t = ?/2.

 

[Deleted member 4993]

Problem:

Let the curve r(t) =< t,cos(t),sin(t) >.
a) What do we call the curve that is the graph of r = r(t)?
b) Find the Frenet Frame of the curve at t = ?/2.
c) Find the curvature of the curve at t = ?/2.
d) Find the parametric equations of the tangent line to the curve at t = ?/2.

Please show us your work - indicating exactly where you are stuck - so that we know where to begin to help you.

 

[koalamath]

a.) I said it was cylinder around the x axis but that isn't right
b). T(pi/2)=1/2^(1/2)i-1/2^(1/2)j
N(pi/2)=1/2^(1/2)k
B(pi/2)=1/2^(1/2)i-1/2^(1/2)j

c) K=1/2
d. is (1,-sint,cost) the tangent line?