Mathematics, Vector Calculus, Learning Mathematics, Math.
climbs, what would the curvature be then? R(t) = cos(t)i + sin(t)j + t/2 k dR/dt = –sin(t)i + cos(t)j + 1/2 k |dR/dt| = ds/dt = sqrt(sin^2(t) + cos^2(t) + 1/4) = sqrt(5/4) = √5/2 T = dR/dt / |dR/dt| = 2/√5 (–sin(t)i + cos(t)j + 1/2 k) dT/dt = 2/√5(–cos(t)i + –sin(t)j) dT/ds = dT/dt / ds/dt =