Question

Find parametric equations for the tangent line at the point (cos(3pi/6),sin(3pi/6), (3pi/6))

Answer 1

$r(t)=(\cos{t},\sin{t},t) \\r'(t)=(-\sin{t},\cos{t},1) \\t= \frac{3\pi}{6} = \frac{\pi}{2} \\ r'(t)=(-\sin{\frac{\pi}{2}},\cos{\frac{\pi}{2}},1) \\ r'(t)=(-1,0,1) \\ \\x=0+t(-1)=-t \\y=1+t\times 0=1 \\z= \frac{\pi}{2} +t$