Show that at every point on the curve r(t) = <(e^(t)cos(t)), (e^(t)sin(t)), e^t> the angle between...

Show that at every point on the curve

r(t) = <(e^(t)*cos(t)), (e^(t)*sin(t)), e^t>

the angle between the unit tangent vector and the z-axis is the same. Then show that the same result holds true for the unit normal and binormal vectors.

Solutions

Expert Solution

milcah answered 1 year ago

Next > < Previous

Related Solutions

For this parametrized curve: x = e^(2t) sin t , y = cos(4t) find tangent line...

For this parametrized curve: x = e^(2t) sin t , y = cos(4t) find tangent line to curve when t=1

Find the point of intersection of the tangent lines to the curve r(t) = 5 sin(πt),...

Find the point of intersection of the tangent lines to the curve r(t) = 5 sin(πt), 2 sin(πt), 6 cos(πt) at the points where t = 0 and t = 0.5. (x, y, z) =

Consider the helix r(t)=(cos(2t),sin(2t),−3t)r(t)=(cos(2t),sin(2t),−3t). Compute, at t=π/6 A. The unit tangent vector T=T= ( , ,...

Consider the helix r(t)=(cos(2t),sin(2t),−3t)r(t)=(cos(2t),sin(2t),−3t). Compute, at t=π/6 A. The unit tangent vector T=T= ( , , ) B. The unit normal vector N=N= ( , , ) C. The unit binormal vector B=B= ( , , ) D. The curvature κ=κ=

The plane curve represented by x(t) = t − sin(t), y(t) = 7 − cos(t), is...

The plane curve represented by x(t) = t − sin(t), y(t) = 7 − cos(t), is a cycloid. (a) Find the slope of the tangent line to the cycloid for 0 < t < 2π. dy dx (b) Find an equation of the tangent line to the cycloid at t = π 3 (c) Find the length of the cycloid from t = 0 to t = π 2

Given r(t) = <2 cos(t), 2 sin(t), 2t>. • What is the arc length of r(t)...

Given r(t) = <2 cos(t), 2 sin(t), 2t>. • What is the arc length of r(t) from t = 0 to t = 5. SET UP integral but DO NOT evaluate • What is the curvature κ(t)?

Let r(t) = (cos(πt), sin(πt), 3t). Calculate r'(t), T(t) and evaluate T(1).

If u(t) = < sin(8t), cos(4t), t > and v(t) = < t, cos(4t), sin(8t) >,...

If u(t) = < sin(8t), cos(4t), t > and v(t) = < t, cos(4t), sin(8t) >, use the formula below to find the given derivative. d/(dt)[u(t)* v(t)] = u'(t)* v(t) + u(t)* v'(t) d/(dt)[u(t) x v(t)] = <.______ , _________ , _______>

If u(t) = < sin(5t), cos(5t), t > and v(t) = < t, cos(5t), sin(5t) >,...

If u(t) = < sin(5t), cos(5t), t > and v(t) = < t, cos(5t), sin(5t) >, use the formula below to find the given derivative. d/dt[ u(t) * v(t)] = u'(t) * v(t) + u(t)* v'(t) d/dt [ u(t) x v(t)] = ?

Given the parametrized curve r(u) = a cos u(1 − cos u)ˆi + a sin u(1...

Given the parametrized curve r(u) = a cos u(1 − cos u)ˆi + a sin u(1 − cos u)ˆj, u ∈ [0, 2π [ , (with a being a constant) i) Sketch the curve (e.g. by constructing a table of values or some other method) ii) Find the tangent vector r 0 (u). What is the tangent vector at u = 0? And at u = 2π? Explain your result. iii) Is the curve regularly parametrized? Motivate your answer using...

show your work. Find the sin t and cos t for t =150o. You may need...

show your work. Find the sin t and cos t for t =150o. You may need to draw the reference angle first, but you only have to enter the sine and cosine values.

Subjects

Question

Show that at every point on the curve r(t) = <(e^(t)*cos(t)), (e^(t)*sin(t)), e^t> the angle between...

Solutions

Expert Solution

Related Solutions

Show that at every point on the curve r(t) = <(e^(t)cos(t)), (e^(t)sin(t)), e^t> the angle between...