Question

Consider the helix r(t) = ⟨cos(7t), sin(7t), -2t⟩. Compute, at t = π/6.

Answer 1

To compute the helix at t = π/6, substitute π/6 for t in the equation r(t) = ⟨cos(7t), sin(7t), -2t⟩: r(π/6) = ⟨-sqrt(3)/2, 1/2, -π/3⟩.

Step-by-step explanation:

To compute the helix at t = π/6, substitute π/6 for t in the equation r(t) = ⟨cos(7t), sin(7t), -2t⟩:

r(π/6) = ⟨cos(7(π/6)), sin(7(π/6)), -2(π/6)⟩

= ⟨cos(7π/6), sin(7π/6), -π/3⟩

= ⟨-sqrt(3)/2, 1/2, -π/3⟩