Let F3={cos⁡(t),sin⁡(t),cos⁡(3t),sin⁡(3t)} and T3={cos3(t),cos2(t)sin(t),cos(t)sin2(t),sin3(t)}. Use the power reduction formulas and the triple angle identities to show...

Let F3={cos⁡(t),sin⁡(t),cos⁡(3t),sin⁡(3t)} and T3={cos3(t),cos2(t)sin(t),cos(t)sin2(t),sin3(t)}. Use the power reduction formulas and the triple angle identities to show the following:

Show T3⊆Span(F3).
Show F3⊆Span(T3).

Expert Solution

Colby Messinger answered 2 years ago

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

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.

Question

Let F3={cos⁡(t),sin⁡(t),cos⁡(3t),sin⁡(3t)} and T3={cos3(t),cos2(t)sin(t),cos(t)sin2(t),sin3(t)}. Use the power reduction formulas and the triple angle identities to show...

Solutions

Expert Solution

Related Solutions

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

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

Question

Let F3={cos⁡(t),sin⁡(t),cos⁡(3t),sin⁡(3t)} and T3={cos3(t),cos2(t)sin(t),cos(t)sin2(t),sin3(t)}. Use the power reduction formulas and the triple angle identities to show...

Solutions

Expert Solution

Related Solutions

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

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...