Parametrised curves in plane and space
General · Mathematics
Study notes
Q: For helix r(t) = (cos t, sin t, t), find speed and arc length 0 to 2π. r'(t) = (-sin t, cos t, 1). Speed: |r'| = √(sin²t+cos²t+1) = √2 (constant!). Arc length: ∫₀^(2π)√2 dt = 2π√2! (Unit tangent: (-sin t,cos t,1)/√2!)